Dynamical Systems
An Introduction
Seiten
2012
Springer London Ltd (Verlag)
978-1-4471-4834-0 (ISBN)
Springer London Ltd (Verlag)
978-1-4471-4834-0 (ISBN)
This concise introduction to dynamical systems contains a large number of examples and exercises. It is an ideal textbook for a one-semester or two-semester course at the advanced undergraduate or beginning graduate levels.
The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction.
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.
The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction.
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.
Introduction.- Basic Notions and Examples.- Topological Dynamics.- Low-Dimensional Dynamics.- Hyperbolic Dynamics I.- Hyperbolic Dynamics II.- Symbolic Dynamics.- Ergodic Theory.
| Reihe/Serie | Universitext |
|---|---|
| Zusatzinfo | 44 Illustrations, black and white; IX, 209 p. 44 illus. |
| Verlagsort | England |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | Dynamisches System • ergodic theory • Hyperbolic dynamics • Low-Dimensional Dynamics • symbolic dynamics • Topological Dynamics |
| ISBN-10 | 1-4471-4834-7 / 1447148347 |
| ISBN-13 | 978-1-4471-4834-0 / 9781447148340 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
was jeder über Informatik wissen sollte
Buch | Softcover (2024)
Springer Vieweg (Verlag)
CHF 53,15
Grundlagen – Anwendungen – Perspektiven
Buch | Softcover (2022)
Springer Vieweg (Verlag)
CHF 48,95
Eine Einführung in die Systemtheorie
Buch | Softcover (2022)
UTB (Verlag)
CHF 34,95
