Hyperbolic flows

by Fisher, Todd,, Professeur de mathématiques

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Title Statements

Full title :Hyperbolic flows / Todd Fisher, Boris Hasselblatt.

Summary

The origins of dynamical systems trace back to flows and differential equations, and this is a modern text and reference on dynamical systems in which continuous-time dynamics is primary. It addresses needs unmet by modern books on dynamical systems, which largely focus on discrete time. Students have lacked a useful introduction to flows, and researchers have difficulty finding references to cite for core results in the theory of flows. Even when these are known substantial diligence and consultation with experts is often needed to find them. This book presents the theory of flows from the topological, smooth, and measurable points of view. The first part introduces the general topological and ergodic theory of flows, and the second part presents the core theory of hyperbolic flows as well as a range of recent developments. Therefore, the book can be used both as a textbook - for either courses or self-study - and as a reference for students and researchers. There are a number of new results in the book, and many more are hard to locate elsewhere, often having appeared only in the original research literature. This book makes them all easily accessible and does so in the context of a comprehensive and coherent presentation of the theory of hyperbolic flows.

Edition Statements

Publication Date:2019.

Publication Statements

Publisher(s):European Mathematical Society Publishing House
Place of Publication:Berlin, Germany
Language:eng
Publication Date:2019.

Notes

In European Mathematical Society.

The Physical Object

Description:1 ressource en ligne (737 pages).

Edition Identifiers

ISBN:9783037197004, 3037197005
oclc:on1157014517
LC Classification:QA901
Dewey Decimal:531.11

Introduction -- I. Flows -- 1. Topological dynamics -- 2. Hyperbolic geodesic flow -- 3. Ergodic theory -- 4. Entropy, pressure, and equilibrium states -- II. Hyperbolic flows -- Introduction to Part II -- 5. Hyperbolicity -- 6. Invariant foliations -- 7. Ergodic theory of hyperbolic sets -- 8. Anosov flows -- 9. Rigidity -- Appendices: A. Measure-theoretic entropy of maps -- B. Hyperbolic maps and invariant manifolds -- Hints and answers to the exercises.

Subjects

Differential equations Differential equations -- Textbooks e-books Équations différentielles -- Manuels d'… Fluid mechanics Fluid mechanics -- Textbooks Livres numériques Manuels d'enseignement supérieur Mécanique des fluides -- Manuels d'ense… Textbooks Théorie des systèmes dynamiques -- Manu…