Topological Dynamical Systems :: an Introduction to the Dynamics of Continuous Mappings /
This book is an elementary introduction to the theory of discrete dynamical systems, also stressing the topological background of the topic. It treats all important concepts needed to understand recent literature from the 'applied general topology' angle. The book is addressed to graduate...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston :
De Gruyter,
[2014]
|
| Schriftenreihe: | De Gruyter studies in mathematics.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book is an elementary introduction to the theory of discrete dynamical systems, also stressing the topological background of the topic. It treats all important concepts needed to understand recent literature from the 'applied general topology' angle. The book is addressed to graduate students and beyond. |
| Beschreibung: | 1 online resource (xv, 498 pages) : illustrations. |
| Bibliographie: | Includes bibliographical references (pages 481-484) and index. |
| ISBN: | 3110342405 9783110342406 |
Internformat
MARC
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| 100 | 1 | |a Vries, Jan de, |e author. | |
| 245 | 1 | 0 | |a Topological Dynamical Systems : |b an Introduction to the Dynamics of Continuous Mappings / |c Jan de Vries. |
| 264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2014] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (xv, 498 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a De Gruyter Studies in Mathematics ; |v volume 59 | |
| 504 | |a Includes bibliographical references (pages 481-484) and index. | ||
| 505 | 0 | |a Preface; Notation; 0 Introduction; 0.1 Definition and a (very brief) historical overview; 0.2 Continuous vs. discrete time; 0.3 The dynamical systems point of view; 0.4 Examples; 1 Basic notions; 1.1 Invariant and periodic points; 1.2 Invariant sets; 1.3 Transitivity; 1.4 Limit sets; 1.5 Topological conjugacy and factor mappings; 1.6 Equicontinuity and weak mixing; 1.7 Miscellaneous examples; 2 Dynamical systems on the real line; 2.1 Graphical iteration; 2.2 Existence of periodic orbits; 2.3 The truncated tent map; 2.4 The double of a mapping. | |
| 505 | 8 | |a 2.5 The Markov graph of a periodic orbit in an interval 2.6 Transitivity of mappings of an interval; 3 Limit behaviour; 3.1 Limit sets and attraction; 3.2 Stability; 3.3 Stability and attraction for periodic orbits; 3.4 Asymptotic stability in locally compact spaces; 3.5 The structure of (asymptotically) stable sets; 4 Recurrent behaviour; 4.1 Recurrent points; 4.2 Almost periodic points and minimal orbit closures; 4.3 Non-wandering points; 4.4 Chain-recurrence; 4.5 Asymptotic stability and basic sets; 5 Shift systems; 5.1 Notation and terminology; 5.2 The shift mapping; 5.3 Shift spaces. | |
| 505 | 8 | |a 5.4 Factor maps 5.5 Subshifts and graphs; 5.6 Recurrence, almost periodicity and mixing; 6 Symbolic representations; 6.1 Topological partitions; 6.2 Expansive systems; 6.3 Applications; 7 Erratic behaviour; 7.1 Stability revisited; 7.2 Chaos(1): sensitive systems; 7.3 Chaos(2): scrambled sets; 7.4 Horseshoes for interval maps; 7.5 Existence of a horseshoe; 8 Topological entropy; 8.1 The definition; 8.2 Independence of the metric; factor maps; 8.3 Maps on intervals and circles; 8.4 The definition with covers; 8.5 Miscellaneous results; 8.6 Positive entropy and horseshoes for interval maps. | |
| 505 | 8 | |a A Topology A.1 Elementary notions; A.2 Compactness; A.3 Continuous mappings; A.4 Convergence; A.5 Subspaces, products and quotients; A.6 Connectedness; A.7 Metric spaces; A.8 Baire category; A.9 Irreduciblemappings; A.10 Miscellaneous results; B The Cantor set; B.1 The construction; B.2 Proof of Brouwer's Theorem; B.3 Cantor spaces; C Hints to the Exercises; Literature; Index. | |
| 520 | |a This book is an elementary introduction to the theory of discrete dynamical systems, also stressing the topological background of the topic. It treats all important concepts needed to understand recent literature from the 'applied general topology' angle. The book is addressed to graduate students and beyond. | ||
| 588 | |a Description based on online resource; title from digital title page (viewed on January 26, 2024). | ||
| 546 | |a English. | ||
| 650 | 0 | |a Topological dynamics. |0 http://id.loc.gov/authorities/subjects/sh85136080 | |
| 650 | 6 | |a Dynamique topologique. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Topological dynamics |2 fast | |
| 650 | 7 | |a Topologische Dynamik |2 gnd |0 http://d-nb.info/gnd/4253345-4 | |
| 653 | |a Almost periodic points and minimal sets. | ||
| 653 | |a Chaos. | ||
| 653 | |a Discrete dynamical systems. | ||
| 653 | |a Recurrence. | ||
| 653 | |a Shift systems and symbolic dynamics. | ||
| 653 | |a Symptotic stability and attraction. | ||
| 653 | |a Topological entropy. | ||
| 776 | 0 | 8 | |i Print version: |a Vries, J. de (Jan). |t Topological dynamical systems. |d Berlin ; Boston : De Gruyter, [2014] |z 9783110340730 |w (DLC) 2013041808 |w (OCoLC)881660419 |
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| contents | Preface; Notation; 0 Introduction; 0.1 Definition and a (very brief) historical overview; 0.2 Continuous vs. discrete time; 0.3 The dynamical systems point of view; 0.4 Examples; 1 Basic notions; 1.1 Invariant and periodic points; 1.2 Invariant sets; 1.3 Transitivity; 1.4 Limit sets; 1.5 Topological conjugacy and factor mappings; 1.6 Equicontinuity and weak mixing; 1.7 Miscellaneous examples; 2 Dynamical systems on the real line; 2.1 Graphical iteration; 2.2 Existence of periodic orbits; 2.3 The truncated tent map; 2.4 The double of a mapping. 2.5 The Markov graph of a periodic orbit in an interval 2.6 Transitivity of mappings of an interval; 3 Limit behaviour; 3.1 Limit sets and attraction; 3.2 Stability; 3.3 Stability and attraction for periodic orbits; 3.4 Asymptotic stability in locally compact spaces; 3.5 The structure of (asymptotically) stable sets; 4 Recurrent behaviour; 4.1 Recurrent points; 4.2 Almost periodic points and minimal orbit closures; 4.3 Non-wandering points; 4.4 Chain-recurrence; 4.5 Asymptotic stability and basic sets; 5 Shift systems; 5.1 Notation and terminology; 5.2 The shift mapping; 5.3 Shift spaces. 5.4 Factor maps 5.5 Subshifts and graphs; 5.6 Recurrence, almost periodicity and mixing; 6 Symbolic representations; 6.1 Topological partitions; 6.2 Expansive systems; 6.3 Applications; 7 Erratic behaviour; 7.1 Stability revisited; 7.2 Chaos(1): sensitive systems; 7.3 Chaos(2): scrambled sets; 7.4 Horseshoes for interval maps; 7.5 Existence of a horseshoe; 8 Topological entropy; 8.1 The definition; 8.2 Independence of the metric; factor maps; 8.3 Maps on intervals and circles; 8.4 The definition with covers; 8.5 Miscellaneous results; 8.6 Positive entropy and horseshoes for interval maps. A Topology A.1 Elementary notions; A.2 Compactness; A.3 Continuous mappings; A.4 Convergence; A.5 Subspaces, products and quotients; A.6 Connectedness; A.7 Metric spaces; A.8 Baire category; A.9 Irreduciblemappings; A.10 Miscellaneous results; B The Cantor set; B.1 The construction; B.2 Proof of Brouwer's Theorem; B.3 Cantor spaces; C Hints to the Exercises; Literature; Index. |
| ctrlnum | (OCoLC)873464768 |
| dewey-full | 515.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.4 |
| dewey-search | 515.4 |
| dewey-sort | 3515.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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ind1="1" ind2=" "><subfield code="a">Vries, Jan de,</subfield><subfield code="e">author.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Topological Dynamical Systems :</subfield><subfield code="b">an Introduction to the Dynamics of Continuous Mappings /</subfield><subfield code="c">Jan de Vries.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ;</subfield><subfield code="a">Boston :</subfield><subfield code="b">De Gruyter,</subfield><subfield code="c">[2014]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2014</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xv, 498 pages) :</subfield><subfield code="b">illustrations.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">De Gruyter Studies in Mathematics ;</subfield><subfield code="v">volume 59</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 481-484) and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Preface; Notation; 0 Introduction; 0.1 Definition and a (very brief) historical overview; 0.2 Continuous vs. discrete time; 0.3 The dynamical systems point of view; 0.4 Examples; 1 Basic notions; 1.1 Invariant and periodic points; 1.2 Invariant sets; 1.3 Transitivity; 1.4 Limit sets; 1.5 Topological conjugacy and factor mappings; 1.6 Equicontinuity and weak mixing; 1.7 Miscellaneous examples; 2 Dynamical systems on the real line; 2.1 Graphical iteration; 2.2 Existence of periodic orbits; 2.3 The truncated tent map; 2.4 The double of a mapping.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.5 The Markov graph of a periodic orbit in an interval 2.6 Transitivity of mappings of an interval; 3 Limit behaviour; 3.1 Limit sets and attraction; 3.2 Stability; 3.3 Stability and attraction for periodic orbits; 3.4 Asymptotic stability in locally compact spaces; 3.5 The structure of (asymptotically) stable sets; 4 Recurrent behaviour; 4.1 Recurrent points; 4.2 Almost periodic points and minimal orbit closures; 4.3 Non-wandering points; 4.4 Chain-recurrence; 4.5 Asymptotic stability and basic sets; 5 Shift systems; 5.1 Notation and terminology; 5.2 The shift mapping; 5.3 Shift spaces.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">5.4 Factor maps 5.5 Subshifts and graphs; 5.6 Recurrence, almost periodicity and mixing; 6 Symbolic representations; 6.1 Topological partitions; 6.2 Expansive systems; 6.3 Applications; 7 Erratic behaviour; 7.1 Stability revisited; 7.2 Chaos(1): sensitive systems; 7.3 Chaos(2): scrambled sets; 7.4 Horseshoes for interval maps; 7.5 Existence of a horseshoe; 8 Topological entropy; 8.1 The definition; 8.2 Independence of the metric; factor maps; 8.3 Maps on intervals and circles; 8.4 The definition with covers; 8.5 Miscellaneous results; 8.6 Positive entropy and horseshoes for interval maps.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">A Topology A.1 Elementary notions; A.2 Compactness; A.3 Continuous mappings; A.4 Convergence; A.5 Subspaces, products and quotients; A.6 Connectedness; A.7 Metric spaces; A.8 Baire category; A.9 Irreduciblemappings; A.10 Miscellaneous results; B The Cantor set; B.1 The construction; B.2 Proof of Brouwer's Theorem; B.3 Cantor spaces; C Hints to the Exercises; 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It treats all important concepts needed to understand recent literature from the 'applied general topology' angle. 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| id | ZDB-4-EBA-ocn873464768 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:51Z |
| institution | BVB |
| isbn | 3110342405 9783110342406 |
| language | English |
| oclc_num | 873464768 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 498 pages) : illustrations. |
| psigel | ZDB-4-EBA |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter studies in mathematics. |
| series2 | De Gruyter Studies in Mathematics ; |
| spelling | Vries, Jan de, author. Topological Dynamical Systems : an Introduction to the Dynamics of Continuous Mappings / Jan de Vries. Berlin ; Boston : De Gruyter, [2014] ©2014 1 online resource (xv, 498 pages) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter Studies in Mathematics ; volume 59 Includes bibliographical references (pages 481-484) and index. Preface; Notation; 0 Introduction; 0.1 Definition and a (very brief) historical overview; 0.2 Continuous vs. discrete time; 0.3 The dynamical systems point of view; 0.4 Examples; 1 Basic notions; 1.1 Invariant and periodic points; 1.2 Invariant sets; 1.3 Transitivity; 1.4 Limit sets; 1.5 Topological conjugacy and factor mappings; 1.6 Equicontinuity and weak mixing; 1.7 Miscellaneous examples; 2 Dynamical systems on the real line; 2.1 Graphical iteration; 2.2 Existence of periodic orbits; 2.3 The truncated tent map; 2.4 The double of a mapping. 2.5 The Markov graph of a periodic orbit in an interval 2.6 Transitivity of mappings of an interval; 3 Limit behaviour; 3.1 Limit sets and attraction; 3.2 Stability; 3.3 Stability and attraction for periodic orbits; 3.4 Asymptotic stability in locally compact spaces; 3.5 The structure of (asymptotically) stable sets; 4 Recurrent behaviour; 4.1 Recurrent points; 4.2 Almost periodic points and minimal orbit closures; 4.3 Non-wandering points; 4.4 Chain-recurrence; 4.5 Asymptotic stability and basic sets; 5 Shift systems; 5.1 Notation and terminology; 5.2 The shift mapping; 5.3 Shift spaces. 5.4 Factor maps 5.5 Subshifts and graphs; 5.6 Recurrence, almost periodicity and mixing; 6 Symbolic representations; 6.1 Topological partitions; 6.2 Expansive systems; 6.3 Applications; 7 Erratic behaviour; 7.1 Stability revisited; 7.2 Chaos(1): sensitive systems; 7.3 Chaos(2): scrambled sets; 7.4 Horseshoes for interval maps; 7.5 Existence of a horseshoe; 8 Topological entropy; 8.1 The definition; 8.2 Independence of the metric; factor maps; 8.3 Maps on intervals and circles; 8.4 The definition with covers; 8.5 Miscellaneous results; 8.6 Positive entropy and horseshoes for interval maps. A Topology A.1 Elementary notions; A.2 Compactness; A.3 Continuous mappings; A.4 Convergence; A.5 Subspaces, products and quotients; A.6 Connectedness; A.7 Metric spaces; A.8 Baire category; A.9 Irreduciblemappings; A.10 Miscellaneous results; B The Cantor set; B.1 The construction; B.2 Proof of Brouwer's Theorem; B.3 Cantor spaces; C Hints to the Exercises; Literature; Index. This book is an elementary introduction to the theory of discrete dynamical systems, also stressing the topological background of the topic. It treats all important concepts needed to understand recent literature from the 'applied general topology' angle. The book is addressed to graduate students and beyond. Description based on online resource; title from digital title page (viewed on January 26, 2024). English. Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Dynamique topologique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Topological dynamics fast Topologische Dynamik gnd http://d-nb.info/gnd/4253345-4 Almost periodic points and minimal sets. Chaos. Discrete dynamical systems. Recurrence. Shift systems and symbolic dynamics. Symptotic stability and attraction. Topological entropy. Print version: Vries, J. de (Jan). Topological dynamical systems. Berlin ; Boston : De Gruyter, [2014] 9783110340730 (DLC) 2013041808 (OCoLC)881660419 De Gruyter studies in mathematics. http://id.loc.gov/authorities/names/n83742913 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=699675 Volltext |
| spellingShingle | Vries, Jan de Topological Dynamical Systems : an Introduction to the Dynamics of Continuous Mappings / De Gruyter studies in mathematics. Preface; Notation; 0 Introduction; 0.1 Definition and a (very brief) historical overview; 0.2 Continuous vs. discrete time; 0.3 The dynamical systems point of view; 0.4 Examples; 1 Basic notions; 1.1 Invariant and periodic points; 1.2 Invariant sets; 1.3 Transitivity; 1.4 Limit sets; 1.5 Topological conjugacy and factor mappings; 1.6 Equicontinuity and weak mixing; 1.7 Miscellaneous examples; 2 Dynamical systems on the real line; 2.1 Graphical iteration; 2.2 Existence of periodic orbits; 2.3 The truncated tent map; 2.4 The double of a mapping. 2.5 The Markov graph of a periodic orbit in an interval 2.6 Transitivity of mappings of an interval; 3 Limit behaviour; 3.1 Limit sets and attraction; 3.2 Stability; 3.3 Stability and attraction for periodic orbits; 3.4 Asymptotic stability in locally compact spaces; 3.5 The structure of (asymptotically) stable sets; 4 Recurrent behaviour; 4.1 Recurrent points; 4.2 Almost periodic points and minimal orbit closures; 4.3 Non-wandering points; 4.4 Chain-recurrence; 4.5 Asymptotic stability and basic sets; 5 Shift systems; 5.1 Notation and terminology; 5.2 The shift mapping; 5.3 Shift spaces. 5.4 Factor maps 5.5 Subshifts and graphs; 5.6 Recurrence, almost periodicity and mixing; 6 Symbolic representations; 6.1 Topological partitions; 6.2 Expansive systems; 6.3 Applications; 7 Erratic behaviour; 7.1 Stability revisited; 7.2 Chaos(1): sensitive systems; 7.3 Chaos(2): scrambled sets; 7.4 Horseshoes for interval maps; 7.5 Existence of a horseshoe; 8 Topological entropy; 8.1 The definition; 8.2 Independence of the metric; factor maps; 8.3 Maps on intervals and circles; 8.4 The definition with covers; 8.5 Miscellaneous results; 8.6 Positive entropy and horseshoes for interval maps. A Topology A.1 Elementary notions; A.2 Compactness; A.3 Continuous mappings; A.4 Convergence; A.5 Subspaces, products and quotients; A.6 Connectedness; A.7 Metric spaces; A.8 Baire category; A.9 Irreduciblemappings; A.10 Miscellaneous results; B The Cantor set; B.1 The construction; B.2 Proof of Brouwer's Theorem; B.3 Cantor spaces; C Hints to the Exercises; Literature; Index. Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Dynamique topologique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Topological dynamics fast Topologische Dynamik gnd http://d-nb.info/gnd/4253345-4 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85136080 http://d-nb.info/gnd/4253345-4 |
| title | Topological Dynamical Systems : an Introduction to the Dynamics of Continuous Mappings / |
| title_auth | Topological Dynamical Systems : an Introduction to the Dynamics of Continuous Mappings / |
| title_exact_search | Topological Dynamical Systems : an Introduction to the Dynamics of Continuous Mappings / |
| title_full | Topological Dynamical Systems : an Introduction to the Dynamics of Continuous Mappings / Jan de Vries. |
| title_fullStr | Topological Dynamical Systems : an Introduction to the Dynamics of Continuous Mappings / Jan de Vries. |
| title_full_unstemmed | Topological Dynamical Systems : an Introduction to the Dynamics of Continuous Mappings / Jan de Vries. |
| title_short | Topological Dynamical Systems : |
| title_sort | topological dynamical systems an introduction to the dynamics of continuous mappings |
| title_sub | an Introduction to the Dynamics of Continuous Mappings / |
| topic | Topological dynamics. http://id.loc.gov/authorities/subjects/sh85136080 Dynamique topologique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Topological dynamics fast Topologische Dynamik gnd http://d-nb.info/gnd/4253345-4 |
| topic_facet | Topological dynamics. Dynamique topologique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Topological dynamics Topologische Dynamik |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=699675 |
| work_keys_str_mv | AT vriesjande topologicaldynamicalsystemsanintroductiontothedynamicsofcontinuousmappings |