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  3. Nonuniform Hyperbolicity
  • Cited by 246
Publisher:
Cambridge University Press
Online publication date:
May 2013
Print publication year:
2007
Online ISBN:
9781107326026
DOI:
https://doi.org/10.1017/CBO9781107326026
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Geometry and Topology
Series:
Encyclopedia of Mathematics and its Applications (115)
Information

Book 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 Teichmüller flows), in rigidity theory, in the study of some partial differential equations (e.g., the Schrödinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields.

Reviews

'… will be indispensable for any mathematically inclined reader with a serious interest in the subject.'

Source: EMS Newsletter

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