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Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem.
The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology.
This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.
Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem.
The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology.
This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.
Short and self-contained introduction to dynamical systems
Direct and rigorous exposition
Contains a large number of examples and exercises
Includes an accessible introduction to ergodic theory
Includes supplementary material: [...]
Introduction.- Basic Notions and Examples.- Topological Dynamics.- Low-Dimensional Dynamics.- Hyperbolic Dynamics I.- Hyperbolic Dynamics II.- Symbolic Dynamics.- Ergodic Theory.
| Erscheinungsjahr: | 2012 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Universitext |
| Inhalt: |
ix
209 S. 44 s/w Illustr. 209 p. 44 illus. |
| ISBN-13: | 9781447148340 |
| ISBN-10: | 1447148347 |
| Sprache: | Englisch |
| Herstellernummer: | 86164764 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Valls, Claudia
Barreira, Luis |
| Hersteller: |
Springer London
Springer-Verlag London Ltd. Universitext |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 13 mm |
| Von/Mit: | Claudia Valls (u. a.) |
| Erscheinungsdatum: | 01.12.2012 |
| Gewicht: | 0,341 kg |
Short and self-contained introduction to dynamical systems
Direct and rigorous exposition
Contains a large number of examples and exercises
Includes an accessible introduction to ergodic theory
Includes supplementary material: [...]
Introduction.- Basic Notions and Examples.- Topological Dynamics.- Low-Dimensional Dynamics.- Hyperbolic Dynamics I.- Hyperbolic Dynamics II.- Symbolic Dynamics.- Ergodic Theory.
| Erscheinungsjahr: | 2012 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Universitext |
| Inhalt: |
ix
209 S. 44 s/w Illustr. 209 p. 44 illus. |
| ISBN-13: | 9781447148340 |
| ISBN-10: | 1447148347 |
| Sprache: | Englisch |
| Herstellernummer: | 86164764 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Valls, Claudia
Barreira, Luis |
| Hersteller: |
Springer London
Springer-Verlag London Ltd. Universitext |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 13 mm |
| Von/Mit: | Claudia Valls (u. a.) |
| Erscheinungsdatum: | 01.12.2012 |
| Gewicht: | 0,341 kg |
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