Periodic Differential Equations in the Plane: A Topological Perspective
Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2019]
|
| Schriftenreihe: | De Gruyter Series in Nonlinear Analysis and Applications
29 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FHA01 FHR01 FKE01 FLA01 TUM01 UBY01 UPA01 FAB01 FCO01 Volltext |
| Zusammenfassung: | Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré–Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book |
| Beschreibung: | 1 online resource (195 pages) |
| ISBN: | 9783110551167 |
| DOI: | 10.1515/9783110551167 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV045947072 | ||
| 003 | DE-604 | ||
| 005 | 20200330 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 190624s2019 |||| o||u| ||||||eng d | ||
| 020 | |a 9783110551167 |9 978-3-11-055116-7 | ||
| 024 | 7 | |a 10.1515/9783110551167 |2 doi | |
| 035 | |a (ZDB-23-DGG)9783110551167 | ||
| 035 | |a (OCoLC)1129922083 | ||
| 035 | |a (DE-599)BVBBV045947072 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-Aug4 |a DE-859 |a DE-860 |a DE-739 |a DE-91 |a DE-898 |a DE-706 |a DE-1043 |a DE-858 | ||
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 100 | 1 | |a Ortega, Rafael |d 1960- |e Verfasser |0 (DE-588)1187262692 |4 aut | |
| 245 | 1 | 0 | |a Periodic Differential Equations in the Plane |b A Topological Perspective |c Rafael Ortega |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a 1 online resource (195 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter Series in Nonlinear Analysis and Applications |v 29 | |
| 520 | |a Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré–Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book | ||
| 650 | 4 | |a Dynamisches System | |
| 650 | 4 | |a Ebene | |
| 650 | 4 | |a Gewöhnliche Differentialgleichung | |
| 650 | 4 | |a Periodische Differentialgleichung | |
| 650 | 4 | |a Topologie | |
| 650 | 7 | |a MATHEMATICS / Differential Equations / General |2 bisacsh | |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Periodische Differentialgleichung |0 (DE-588)4503299-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ebene |0 (DE-588)4150968-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Topologie |0 (DE-588)4060425-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Periodische Differentialgleichung |0 (DE-588)4503299-3 |D s |
| 689 | 0 | 1 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | 2 | |a Ebene |0 (DE-588)4150968-7 |D s |
| 689 | 0 | 3 | |a Topologie |0 (DE-588)4060425-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-3-11-055040-5 |
| 830 | 0 | |a De Gruyter Series in Nonlinear Analysis and Applications |v 29 |w (DE-604)BV044970340 |9 29 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9783110551167 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-23-DGG |a ZDB-23-DMA | ||
| 940 | 1 | |q ZDB-23-DMA19 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-031329227 | ||
| 966 | e | |u https://doi.org/10.1515/9783110551167 |l FAW01 |p ZDB-23-DGG |q FAW_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110551167 |l FHA01 |p ZDB-23-DGG |q FHA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110551167 |l FHR01 |p ZDB-23-DMA |q ZDB-23-DMA19 |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110551167 |l FKE01 |p ZDB-23-DGG |q FKE_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110551167 |l FLA01 |p ZDB-23-DGG |q FLA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110551167 |l TUM01 |p ZDB-23-DMA |q TUM_Paketkauf |x Verlag |3 Volltext | |
| 966 | e | |u https://www.degruyter.com/view/product/490214 |l UBY01 |p ZDB-23-DMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110551167 |l UPA01 |p ZDB-23-DGG |q UPA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110551167 |l FAB01 |p ZDB-23-DGG |q FAB_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783110551167 |l FCO01 |p ZDB-23-DGG |q FCO_PDA_DGG |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804180153029361664 |
|---|---|
| any_adam_object | |
| author | Ortega, Rafael 1960- |
| author_GND | (DE-588)1187262692 |
| author_facet | Ortega, Rafael 1960- |
| author_role | aut |
| author_sort | Ortega, Rafael 1960- |
| author_variant | r o ro |
| building | Verbundindex |
| bvnumber | BV045947072 |
| classification_rvk | SK 520 |
| collection | ZDB-23-DGG ZDB-23-DMA |
| ctrlnum | (ZDB-23-DGG)9783110551167 (OCoLC)1129922083 (DE-599)BVBBV045947072 |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9783110551167 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05037nmm a2200685zcb4500</leader><controlfield tag="001">BV045947072</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200330 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">190624s2019 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110551167</subfield><subfield code="9">978-3-11-055116-7</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9783110551167</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-23-DGG)9783110551167</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1129922083</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV045947072</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-Aug4</subfield><subfield code="a">DE-859</subfield><subfield code="a">DE-860</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-1043</subfield><subfield code="a">DE-858</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ortega, Rafael</subfield><subfield code="d">1960-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1187262692</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Periodic Differential Equations in the Plane</subfield><subfield code="b">A Topological Perspective</subfield><subfield code="c">Rafael Ortega</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ; Boston</subfield><subfield code="b">De Gruyter</subfield><subfield code="c">[2019]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2019</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (195 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">De Gruyter Series in Nonlinear Analysis and Applications</subfield><subfield code="v">29</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré–Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dynamisches System</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ebene</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gewöhnliche Differentialgleichung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Periodische Differentialgleichung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topologie</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Differential Equations / General</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Dynamisches System</subfield><subfield code="0">(DE-588)4013396-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Periodische Differentialgleichung</subfield><subfield code="0">(DE-588)4503299-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ebene</subfield><subfield code="0">(DE-588)4150968-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologie</subfield><subfield code="0">(DE-588)4060425-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Periodische Differentialgleichung</subfield><subfield code="0">(DE-588)4503299-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Dynamisches System</subfield><subfield code="0">(DE-588)4013396-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Ebene</subfield><subfield code="0">(DE-588)4150968-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Topologie</subfield><subfield code="0">(DE-588)4060425-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-3-11-055040-5</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter Series in Nonlinear Analysis and Applications</subfield><subfield code="v">29</subfield><subfield code="w">(DE-604)BV044970340</subfield><subfield code="9">29</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield><subfield code="a">ZDB-23-DMA</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-23-DMA19</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-031329227</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAW_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="l">FHA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FHA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="l">FHR01</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="q">ZDB-23-DMA19</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="l">FKE01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FKE_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="l">FLA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FLA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="l">TUM01</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="q">TUM_Paketkauf</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://www.degruyter.com/view/product/490214</subfield><subfield code="l">UBY01</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="l">UPA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">UPA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="l">FAB01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAB_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783110551167</subfield><subfield code="l">FCO01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FCO_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV045947072 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:31:14Z |
| institution | BVB |
| isbn | 9783110551167 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031329227 |
| oclc_num | 1129922083 |
| open_access_boolean | |
| owner | DE-1046 DE-Aug4 DE-859 DE-860 DE-739 DE-91 DE-BY-TUM DE-898 DE-BY-UBR DE-706 DE-1043 DE-858 |
| owner_facet | DE-1046 DE-Aug4 DE-859 DE-860 DE-739 DE-91 DE-BY-TUM DE-898 DE-BY-UBR DE-706 DE-1043 DE-858 |
| physical | 1 online resource (195 pages) |
| psigel | ZDB-23-DGG ZDB-23-DMA ZDB-23-DMA19 ZDB-23-DGG FAW_PDA_DGG ZDB-23-DGG FHA_PDA_DGG ZDB-23-DMA ZDB-23-DMA19 ZDB-23-DGG FKE_PDA_DGG ZDB-23-DGG FLA_PDA_DGG ZDB-23-DMA TUM_Paketkauf ZDB-23-DGG UPA_PDA_DGG ZDB-23-DGG FAB_PDA_DGG ZDB-23-DGG FCO_PDA_DGG |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter Series in Nonlinear Analysis and Applications |
| series2 | De Gruyter Series in Nonlinear Analysis and Applications |
| spelling | Ortega, Rafael 1960- Verfasser (DE-588)1187262692 aut Periodic Differential Equations in the Plane A Topological Perspective Rafael Ortega Berlin ; Boston De Gruyter [2019] © 2019 1 online resource (195 pages) txt rdacontent c rdamedia cr rdacarrier De Gruyter Series in Nonlinear Analysis and Applications 29 Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré–Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book Dynamisches System Ebene Gewöhnliche Differentialgleichung Periodische Differentialgleichung Topologie MATHEMATICS / Differential Equations / General bisacsh Dynamisches System (DE-588)4013396-5 gnd rswk-swf Periodische Differentialgleichung (DE-588)4503299-3 gnd rswk-swf Ebene (DE-588)4150968-7 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Periodische Differentialgleichung (DE-588)4503299-3 s Dynamisches System (DE-588)4013396-5 s Ebene (DE-588)4150968-7 s Topologie (DE-588)4060425-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-3-11-055040-5 De Gruyter Series in Nonlinear Analysis and Applications 29 (DE-604)BV044970340 29 https://doi.org/10.1515/9783110551167 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Ortega, Rafael 1960- Periodic Differential Equations in the Plane A Topological Perspective De Gruyter Series in Nonlinear Analysis and Applications Dynamisches System Ebene Gewöhnliche Differentialgleichung Periodische Differentialgleichung Topologie MATHEMATICS / Differential Equations / General bisacsh Dynamisches System (DE-588)4013396-5 gnd Periodische Differentialgleichung (DE-588)4503299-3 gnd Ebene (DE-588)4150968-7 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4503299-3 (DE-588)4150968-7 (DE-588)4060425-1 |
| title | Periodic Differential Equations in the Plane A Topological Perspective |
| title_auth | Periodic Differential Equations in the Plane A Topological Perspective |
| title_exact_search | Periodic Differential Equations in the Plane A Topological Perspective |
| title_full | Periodic Differential Equations in the Plane A Topological Perspective Rafael Ortega |
| title_fullStr | Periodic Differential Equations in the Plane A Topological Perspective Rafael Ortega |
| title_full_unstemmed | Periodic Differential Equations in the Plane A Topological Perspective Rafael Ortega |
| title_short | Periodic Differential Equations in the Plane |
| title_sort | periodic differential equations in the plane a topological perspective |
| title_sub | A Topological Perspective |
| topic | Dynamisches System Ebene Gewöhnliche Differentialgleichung Periodische Differentialgleichung Topologie MATHEMATICS / Differential Equations / General bisacsh Dynamisches System (DE-588)4013396-5 gnd Periodische Differentialgleichung (DE-588)4503299-3 gnd Ebene (DE-588)4150968-7 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Dynamisches System Ebene Gewöhnliche Differentialgleichung Periodische Differentialgleichung Topologie MATHEMATICS / Differential Equations / General |
| url | https://doi.org/10.1515/9783110551167 |
| volume_link | (DE-604)BV044970340 |
| work_keys_str_mv | AT ortegarafael periodicdifferentialequationsintheplaneatopologicalperspective |