Hyperbolic Flows.

Format:

Book

Author/Creator:

Fisher, Author.

Hasselblatt, Boris, author.

Series:

Zurich Lectures in Advanced Mathematics (ZLAM)

Zurich Lectures in Advanced Mathematics (zlam) 25 2943-4971

Language:

English

Subjects (All):

Dynamics.

Differential equations.

Dynamical systems and ergodic theory.

Physical Description:

1 online resource (737 pages)

Place of Publication:

EMS Press 2019

Zuerich, Switzerland : European Mathematical Society Publishing House, 2019.

Language Note:

English

System Details:

text file PDF

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.

Contents:

I. Flows

Topological dynamics

Hyperbolic geodesic flow

Ergodic theory

Entropy, pressure, and equilibrium states

II. Hyperbolic flows

Hyperbolicity

Invariant foliations

Ergodic theory of hyperbolic sets

Anosov flows

Rigidity.

ISBN:

3-03719-700-5