Nonuniform hyperbolicity: dynamics of systems with nonzero Lyapunov exponents
Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical foundation for the phenomenon known as deterministi...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 115 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical foundation for the phenomenon known as deterministic chaos - the appearance of 'chaotic' motions in pure deterministic dynamical systems. A sufficiently complete description of topological and ergodic properties of systems exhibiting deterministic chaos can be deduced from relatively weak requirements on their local behavior known as nonuniform hyperbolicity conditions. Nonuniform hyperbolicity theory is an important part of the general theory of dynamical systems. Its core is the study of dynamical systems with nonzero Lyapunov exponents both conservative and dissipative, in addition to cocycles and group actions. The results of this theory are widely used in geometry (e.g., geodesic flows and Teichmüller flows), in rigidity theory, in the study of some partial differential equations (e.g., the Schrödinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xiv, 513 pages) |
| ISBN: | 9781107326026 |
| DOI: | 10.1017/CBO9781107326026 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043941853 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2007 |||| o||u| ||||||eng d | ||
| 020 | |a 9781107326026 |c Online |9 978-1-107-32602-6 | ||
| 024 | 7 | |a 10.1017/CBO9781107326026 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781107326026 | ||
| 035 | |a (OCoLC)852633807 | ||
| 035 | |a (DE-599)BVBBV043941853 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 531/.11 |2 22 | |
| 084 | |a SK 810 |0 (DE-625)143257: |2 rvk | ||
| 100 | 1 | |a Barreira, Luis |d 1968- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonuniform hyperbolicity |b dynamics of systems with nonzero Lyapunov exponents |c Luis Barreira, Yakov Pesin |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2007 | |
| 300 | |a 1 online resource (xiv, 513 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Encyclopedia of mathematics and its applications |v volume 115 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Concepts of nonuniform hyperbolicity -- Lyapunov exponents for linear extensions -- Regularity of cocycles -- Methods for estimating exponents -- The derivative cocyle -- Examples of systems with hyperbolic behavior -- Stable manifold theory -- Basic properties of stable and unstable manifolds -- Smooth measures -- Measure-theoretic entropy and lyapunov exponents -- Stable ergodicity and lyapunov exponents. more examples of systems with nonzero exponents -- Geodesic flows -- SRB measures -- Hyperbolic measure: entropy and dimension -- Hyperbolic measures: topological properties | |
| 520 | |a Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical foundation for the phenomenon known as deterministic chaos - the appearance of 'chaotic' motions in pure deterministic dynamical systems. A sufficiently complete description of topological and ergodic properties of systems exhibiting deterministic chaos can be deduced from relatively weak requirements on their local behavior known as nonuniform hyperbolicity conditions. Nonuniform hyperbolicity theory is an important part of the general theory of dynamical systems. Its core is the study of dynamical systems with nonzero Lyapunov exponents both conservative and dissipative, in addition to cocycles and group actions. The results of this theory are widely used in geometry (e.g., geodesic flows and Teichmüller flows), in rigidity theory, in the study of some partial differential equations (e.g., the Schrödinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields | ||
| 650 | 4 | |a Lyapunov exponents | |
| 650 | 4 | |a Lyapunov stability | |
| 650 | 4 | |a Dynamics | |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Exponent |0 (DE-588)4123668-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hyperbolizität |0 (DE-588)4710615-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | 1 | |a Hyperbolizität |0 (DE-588)4710615-3 |D s |
| 689 | 0 | 2 | |a Ljapunov-Exponent |0 (DE-588)4123668-3 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Pesin, Ya. B. |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-83258-8 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9781107326026 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029350823 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1017/CBO9781107326026 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9781107326026 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176884082147328 |
|---|---|
| any_adam_object | |
| author | Barreira, Luis 1968- |
| author_facet | Barreira, Luis 1968- |
| author_role | aut |
| author_sort | Barreira, Luis 1968- |
| author_variant | l b lb |
| building | Verbundindex |
| bvnumber | BV043941853 |
| classification_rvk | SK 810 |
| collection | ZDB-20-CBO |
| contents | Concepts of nonuniform hyperbolicity -- Lyapunov exponents for linear extensions -- Regularity of cocycles -- Methods for estimating exponents -- The derivative cocyle -- Examples of systems with hyperbolic behavior -- Stable manifold theory -- Basic properties of stable and unstable manifolds -- Smooth measures -- Measure-theoretic entropy and lyapunov exponents -- Stable ergodicity and lyapunov exponents. more examples of systems with nonzero exponents -- Geodesic flows -- SRB measures -- Hyperbolic measure: entropy and dimension -- Hyperbolic measures: topological properties |
| ctrlnum | (ZDB-20-CBO)CR9781107326026 (OCoLC)852633807 (DE-599)BVBBV043941853 |
| dewey-full | 531/.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531/.11 |
| dewey-search | 531/.11 |
| dewey-sort | 3531 211 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9781107326026 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03987nmm a2200553zcb4500</leader><controlfield tag="001">BV043941853</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2007 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107326026</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-107-32602-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9781107326026</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781107326026</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)852633807</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043941853</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-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">531/.11</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 810</subfield><subfield code="0">(DE-625)143257:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Barreira, Luis</subfield><subfield code="d">1968-</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonuniform hyperbolicity</subfield><subfield code="b">dynamics of systems with nonzero Lyapunov exponents</subfield><subfield code="c">Luis Barreira, Yakov Pesin</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xiv, 513 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="0" ind2=" "><subfield code="a">Encyclopedia of mathematics and its applications</subfield><subfield code="v">volume 115</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Concepts of nonuniform hyperbolicity -- Lyapunov exponents for linear extensions -- Regularity of cocycles -- Methods for estimating exponents -- The derivative cocyle -- Examples of systems with hyperbolic behavior -- Stable manifold theory -- Basic properties of stable and unstable manifolds -- Smooth measures -- Measure-theoretic entropy and lyapunov exponents -- Stable ergodicity and lyapunov exponents. more examples of systems with nonzero exponents -- Geodesic flows -- SRB measures -- Hyperbolic measure: entropy and dimension -- Hyperbolic measures: topological properties</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical foundation for the phenomenon known as deterministic chaos - the appearance of 'chaotic' motions in pure deterministic dynamical systems. A sufficiently complete description of topological and ergodic properties of systems exhibiting deterministic chaos can be deduced from relatively weak requirements on their local behavior known as nonuniform hyperbolicity conditions. Nonuniform hyperbolicity theory is an important part of the general theory of dynamical systems. Its core is the study of dynamical systems with nonzero Lyapunov exponents both conservative and dissipative, in addition to cocycles and group actions. The results of this theory are widely used in geometry (e.g., geodesic flows and Teichmüller flows), in rigidity theory, in the study of some partial differential equations (e.g., the Schrödinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lyapunov exponents</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lyapunov stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dynamics</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">Ljapunov-Exponent</subfield><subfield code="0">(DE-588)4123668-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hyperbolizität</subfield><subfield code="0">(DE-588)4710615-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><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="1"><subfield code="a">Hyperbolizität</subfield><subfield code="0">(DE-588)4710615-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Ljapunov-Exponent</subfield><subfield code="0">(DE-588)4123668-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pesin, Ya. B.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-83258-8</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9781107326026</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-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029350823</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781107326026</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781107326026</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043941853 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781107326026 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350823 |
| oclc_num | 852633807 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xiv, 513 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Barreira, Luis 1968- Verfasser aut Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Luis Barreira, Yakov Pesin Cambridge Cambridge University Press 2007 1 online resource (xiv, 513 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 115 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Concepts of nonuniform hyperbolicity -- Lyapunov exponents for linear extensions -- Regularity of cocycles -- Methods for estimating exponents -- The derivative cocyle -- Examples of systems with hyperbolic behavior -- Stable manifold theory -- Basic properties of stable and unstable manifolds -- Smooth measures -- Measure-theoretic entropy and lyapunov exponents -- Stable ergodicity and lyapunov exponents. more examples of systems with nonzero exponents -- Geodesic flows -- SRB measures -- Hyperbolic measure: entropy and dimension -- Hyperbolic measures: topological properties Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical foundation for the phenomenon known as deterministic chaos - the appearance of 'chaotic' motions in pure deterministic dynamical systems. A sufficiently complete description of topological and ergodic properties of systems exhibiting deterministic chaos can be deduced from relatively weak requirements on their local behavior known as nonuniform hyperbolicity conditions. Nonuniform hyperbolicity theory is an important part of the general theory of dynamical systems. Its core is the study of dynamical systems with nonzero Lyapunov exponents both conservative and dissipative, in addition to cocycles and group actions. The results of this theory are widely used in geometry (e.g., geodesic flows and Teichmüller flows), in rigidity theory, in the study of some partial differential equations (e.g., the Schrödinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields Lyapunov exponents Lyapunov stability Dynamics Dynamisches System (DE-588)4013396-5 gnd rswk-swf Ljapunov-Exponent (DE-588)4123668-3 gnd rswk-swf Hyperbolizität (DE-588)4710615-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Hyperbolizität (DE-588)4710615-3 s Ljapunov-Exponent (DE-588)4123668-3 s 1\p DE-604 Pesin, Ya. B. Sonstige oth Erscheint auch als Druckausgabe 978-0-521-83258-8 https://doi.org/10.1017/CBO9781107326026 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Barreira, Luis 1968- Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Concepts of nonuniform hyperbolicity -- Lyapunov exponents for linear extensions -- Regularity of cocycles -- Methods for estimating exponents -- The derivative cocyle -- Examples of systems with hyperbolic behavior -- Stable manifold theory -- Basic properties of stable and unstable manifolds -- Smooth measures -- Measure-theoretic entropy and lyapunov exponents -- Stable ergodicity and lyapunov exponents. more examples of systems with nonzero exponents -- Geodesic flows -- SRB measures -- Hyperbolic measure: entropy and dimension -- Hyperbolic measures: topological properties Lyapunov exponents Lyapunov stability Dynamics Dynamisches System (DE-588)4013396-5 gnd Ljapunov-Exponent (DE-588)4123668-3 gnd Hyperbolizität (DE-588)4710615-3 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4123668-3 (DE-588)4710615-3 |
| title | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents |
| title_auth | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents |
| title_exact_search | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents |
| title_full | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Luis Barreira, Yakov Pesin |
| title_fullStr | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Luis Barreira, Yakov Pesin |
| title_full_unstemmed | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Luis Barreira, Yakov Pesin |
| title_short | Nonuniform hyperbolicity |
| title_sort | nonuniform hyperbolicity dynamics of systems with nonzero lyapunov exponents |
| title_sub | dynamics of systems with nonzero Lyapunov exponents |
| topic | Lyapunov exponents Lyapunov stability Dynamics Dynamisches System (DE-588)4013396-5 gnd Ljapunov-Exponent (DE-588)4123668-3 gnd Hyperbolizität (DE-588)4710615-3 gnd |
| topic_facet | Lyapunov exponents Lyapunov stability Dynamics Dynamisches System Ljapunov-Exponent Hyperbolizität |
| url | https://doi.org/10.1017/CBO9781107326026 |
| work_keys_str_mv | AT barreiraluis nonuniformhyperbolicitydynamicsofsystemswithnonzerolyapunovexponents AT pesinyab nonuniformhyperbolicitydynamicsofsystemswithnonzerolyapunovexponents |