Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero by Luis Barreira,Yakov Pesin

By Luis Barreira,Yakov Pesin

Designed to paintings as a reference and as a complement to a complicated path on dynamical structures, this publication offers a self-contained and entire account of recent delicate ergodic idea. between different issues, this offers a rigorous mathematical beginning for the phenomenon referred to as deterministic chaos - the looks of 'chaotic' motions in natural deterministic dynamical structures. A sufficiently whole description of topological and ergodic homes of structures showing deterministic chaos should be deduced from quite vulnerable necessities on their neighborhood habit often called nonuniform hyperbolicity stipulations. Nonuniform hyperbolicity idea is a crucial a part of the final idea of dynamical structures. Its middle is the research of dynamical structures with nonzero Lyapunov exponents either conservative and dissipative, as well as cocycles and workforce activities. the result of this thought are usual in geometry (e.g., geodesic flows and Teichmüller flows), in tension conception, within the examine of a few partial differential equations (e.g., the Schrödinger equation), within the concept of billiards, in addition to in functions to physics, biology, engineering, and different fields.

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