Dynamical Systems

An Introduction

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book Dynamical Systems by Luis Barreira, Claudia Valls, Springer London
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Luis Barreira, Claudia Valls ISBN: 9781447148357
Publisher: Springer London Publication: December 2, 2012
Imprint: Springer Language: English
Author: Luis Barreira, Claudia Valls
ISBN: 9781447148357
Publisher: Springer London
Publication: December 2, 2012
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer London

Cover of the book Cancer Chemotherapy: an Introduction by Luis Barreira, Claudia Valls
Cover of the book Oxalate Metabolism in Relation to Urinary Stone by Luis Barreira, Claudia Valls
Cover of the book Electromagnetic Behaviour of Metallic Wire Structures by Luis Barreira, Claudia Valls
Cover of the book Multimodality Imaging for Transcatheter Aortic Valve Replacement by Luis Barreira, Claudia Valls
Cover of the book Guide to Teaching Puzzle-based Learning by Luis Barreira, Claudia Valls
Cover of the book Programming Language Concepts by Luis Barreira, Claudia Valls
Cover of the book Specification of Software Systems by Luis Barreira, Claudia Valls
Cover of the book Autonomic Computing by Luis Barreira, Claudia Valls
Cover of the book Computational Social Networks by Luis Barreira, Claudia Valls
Cover of the book Pervasive Advertising by Luis Barreira, Claudia Valls
Cover of the book Assessment of Power System Reliability by Luis Barreira, Claudia Valls
Cover of the book Frontiers in Fusion Research by Luis Barreira, Claudia Valls
Cover of the book Visual Texture by Luis Barreira, Claudia Valls
Cover of the book Heart Failure in Congenital Heart Disease: by Luis Barreira, Claudia Valls
Cover of the book PEM Fuel Cells with Bio-Ethanol Processor Systems by Luis Barreira, Claudia Valls
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy