Description: Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical foundation for the phenomenon known as deterministic chaos - the appearance of 'chaotic' motions in pure deterministic dynamical systems. A sufficiently complete description of topological and ergodic properties of systems exhibiting deterministic chaos can be deduced from relatively weak requirements on their local behavior known as nonuniform hyperbolicity conditions. Nonuniform hyperbolicity theory is an important part of the general theory of dynamical systems. Its core is the study of dynamical systems with nonzero Lyapunov exponents both conservative and dissipative, in addition to cocycles and group actions. The results of this theory are widely used in geometry (e.g., geodesic flows and Teichmuller flows), in rigidity theory, in the study of some partial differential equations (e.g., the Schroedinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields.
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EAN: 9780521832588
UPC: 9780521832588
ISBN: 9780521832588
MPN: N/A
Number of Pages: 528 Pages
Publication Name: Nonuniform Hyperbolicity : Dynamics of Systems with Nonzero Lyapunov Exponents
Language: English
Publisher: Cambridge University Press
Publication Year: 2007
Subject: Differential Equations / General, Mechanics / Dynamics, General
Item Height: 1.3 in
Type: Textbook
Item Weight: 35 Oz
Author: Luis Barreira, Yakov Pesin
Subject Area: Mathematics, Science
Item Length: 9.2 in
Item Width: 6.1 in
Series: Encyclopedia of Mathematics and Its Applications Ser.
Format: Hardcover