Nonuniform Hyperbolicity: Ergodic Theory of Smooth and SRB Measures
Nonuniform Hyperbolicity: Ergodic Theory of Smooth and SRB Measures
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DOI：
10.1017/cbo9781107326026
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
L. Barreira;Y. Pesin
中科院分区：
文献类型：
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作者：
L. Barreira;Y. Pesin
< jats: p>旨在作为一个参考工作，并作为一个补充，以先进的动力系统课程，这本书提出了一个独立的和全面的现代光滑遍历理论。除此之外，这为被称为确定性混沌的现象提供了严格的数学基础-在纯确定性动力系统中出现“混沌”运动。表现出确定性混沌的系统的拓扑和遍历性质的充分完整的描述可以从相对较弱的要求，他们的本地行为被称为非均匀双曲性条件。非一致双曲性理论是动力系统一般理论的重要组成部分。它的核心是研究具有非零李雅普诺夫指数的保守和耗散动力系统，以及上循环和群作用。这一理论的结果被广泛应用于几何学（如测地线流和泰希米勒流），在刚性理论，在一些偏微分方程的研究（如薛定谔方程），在理论的台球，以及在应用物理学，生物学，工程，和其他领域。
< jats: p> 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 (eg, geodesic flows and Teichmüller flows), in rigidity theory, in the study of some partial differential equations (eg, the Schrödinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields.