本书是关于光滑遍历理论的首次系统介绍。它由两部分组成：第一部分介绍了理论核心，第二部分讨论了更高级的主题。特别是，书中描述了Lyapunov指数的一般理论及其在微分方程稳定性理论中的应用、非均匀双曲性的概念、稳定流形理论（着重介绍不变叶状结构的绝对连续性）以及具有非零Lyapunov指数的动力系统的遍历理论。作者还详细描述了所有具有非零Lyapunov指数的保守系统的基本例子，包括在非正曲率紧曲面上的测地线流。
本书是Lyapunov Exponents and Smooth Ergodic Theory的修订和大幅扩展版，面向专攻动力系统和遍历理论的研究生，以及任何想要掌握光滑遍历理论并学会使用其工具的人士。本书设有80多个练习题，可用作光滑遍历理论高级课程的主要教材。本书内容自封，读者只需要基本的实分析、测度论、微分方程和拓扑学的知识，即便如此，作者仍然提供了读者所需的背景定义和结果。

Preface
Part 1.The Core of the Theory
Chapter 1.Examples of Hyperbolic Dynamical Systems
§1.1.Anosov diffeomorphisms
§1.2.Anosov flows
§1.3.The Katok map of the 2-torus
§1.4.Diffeomorphisms with nonzero Lyapunov exponents on surfaces
§1.5.A flow with nonzero Lyapunov exponents
Chapter 2.General Theory of Lyapunov Exponents
§2.1.Lyapunov exponents and their basic properties
§2.2.The Lyapunov and Perron regularity coefficients
§2.3.Lyapunov exponents for linear differential equations
§2.4.Forward and backward regularity.The Lyapunov-Perron regularity
§2.5.Lyapunov exponents for sequences of matrices
Chapter 3.Lyapunov Stability Theory of Nonautonomous Equations
§3.1.Stability of solutions of ordinary differential equations
§3.2.Lyapunov absolute stability theorem
§3.3.Lyapunov conditional stability theorem
Chapter 4.Elements of the Nonuniform Hyperbolicity Theory
§4.1.Dynamical systems with nonzero Lyapunov exponents
§4.2.Nonuniform complete hyperbolicity
§4.3.Regular sets
§4.4.Nonuniform partial hyperbolicity
§4.5.HSlder continuity of invariant distributions
Chapter 5.Cocycles over Dynamical Systems
§5.1.Cocycles and linear extensions
§5.2.Lyapunov exponents and Lyapunov-Perron regularity for cocycles
§5.3.Examples of measurable cocycles over dynamical systems
Chapter 6.The Multiplicative Ergodic Theorem
§6.1.Lyapunov-Perron regularity for sequences of triangular matrices
§6.2.Proof of the Multiplicative Ergodic Theorem
§6.3.Normal forms of measurable cocycles
§6.4.Lyapunov charts
Chapter 7.Local Manifold Theory
§7.1.Local stable manifolds
§7.2.An abstract version of the Stable Manifold Theorem
§7.3.Basic properties of stable and unstable manifolds
Chapter 8.Absolute Continuity of Local Manifolds
§8.1.Absolute continuity of the holonomy map
§8.2.A proof of the absolute continuity theorem
§8.3.Computing the Jacobian of the holonomy map
§8.4.An invariant foliation that is not absolutely continuous
Chapter 9.Ergodic Properties of Smooth Hyperbolic Measures
§9.1.Ergodicity of smooth hyperbolic measures
§9.2.Local ergodicity
§9.3.The entropy formula
Chapter 10.Geodesic Flows on Surfaces of Nonpositive Curvature
§10.1.Preliminary information from Riemannian geometry
§10.2.Definition and local properties of geodesic flows
§10.3.Hyperbolic properties and Lyapunov exponents
§10.4.Ergodic properties
§10.5.The entropy formula for geodesic flows
Part 2.Selected Advanced Topics
Chapter 11.Cone Technics
§11.1.Introduction
§11.2.Lyapunov functions
§11.3.Cocycles with values in the symplectic group
Chapter 12.Partially Hyperbolic Diffeomorphisms with Nonzero Exponents
§12.1.Partial hyperbolicity
§12.2.Systems with negative central exponents
§12.3.Foliations that are not absolutely continuous
Chapter 13.More Examples of Dynamical Systems with Nonzero Lyapunov Exponents
§13.1.Hyperbolic diffeomorphisms with countably many ergodic
components
§13.2.The Shub-Wilkinson map
Chapter 14.Anosov Rigidity
§14.1.The Anosov rigidity phenomenon.I
§14.2.The Anosov rigidity phenomenon.II
Chapter 15.C1 Pathological Behavior: Pugh's Example
Bibliography
Index