本书分为三个部分，第一部分内容验证了内谐零流形M的（连续）自映射f：M→M的阿诺索夫关系，回顾了内诣零流形的主要性质和定义，还展示了内诣零流形与可解流形是不同的；第二部分内容给出了有两种可能的方式去推广阿诺索夫定理，第一种方式是寻找流形类，而不是诣零流形，这就使该关系对已知流形的所有连续映射都成立；第三部分内容集中讨论了低维内诣流形，也就是4维内诣流形，几乎为每个比伯巴赫群提供了特殊比伯巴赫群（或内诣零流形）的阿诺索夫关系的证明或反例。

Preface
Part I Preliminaries
1 Maps of infra-nilmanifolds: an algebraic description
1.1 Lie groups
1.2 Infra-nilmanifolds
1.3 Maps of infra-nilmanifolds
2 The Anosov relation
2.1 Fixed point theory
2.1.1 The Lefschetz number
2.1.2 The Nielsen number
2.1.3 The Anosov relation
2.2 Fixed point theory on infra-nilmanifolds
Part II The results
3 Periodic sequences and infra-nilmanifolds with an odd order holonomy group
3.1 The Anosov theorem for infra-nilmanifolds with odd order holonomy group
3.2 Classes of maps for which the Anosov theorem hold
3.2.1 The Anosov relation for expanding maps
3.2.2 The Anosov relation for nowhere expanding maps
3.3 Infra-nilmanifolds are more complicated
4 Anosov diffeomorphisms
4.1 Algebraic characterization
4.2 Non-primitive fiat manifolds
4.2.1 Flat n-dinensional manifolds with first Betti number smaller than n - 2
4.2.2 Flat manifolds with first Betti number equal to n - 2
4.3 Primitive fiat manifolds
4.3.1 Primitive fiat manifolds in dimension n > 6
4.3.2 Primitive fiat manifolds in dimension 6
5 Infra-nilmanifolds with cyclic holonomy group
5.1 Cyclic groups of matrices
5.2 The Anosov theorem for infra-nilmanifolds with cyclic holonomy group
5.3 The sharpness of the main result for fiat manifolds
6 Generalized Hantzsche-Wendt manifolds
6.1 Definition and properties
6.2 Orientable fiat GHW manifolds
Part III The Anosov theorem in small dimensions
7 Flat manifolds
7.1 General overview in dimension 3 and 4
7.2 Flat manifolds in dimension 4 with Z2 + Z2 as holonomy group
7.3 Flat manifolds in dimension 4 with non-abelian holonomy group
8 Infra-nilmanifolds
8.1 Calculations on 4 dimensional infra-nilmanifolds
8.1.1 2-step nilpotent infra-nilmanifolds
8.1.2 3-step nilpotent infra-nilmanifolds
8.2 The 3-dimensional, 2-step infra-nilmanifolds
8.3 The 4-dimensional, 2-step infra-nilmanifolds
8.3.1 Abelian holonomy group
8.3.2 Non-abelian holonomy group
8.4 The 4-dimensional, 3-step infra-nilmanifolds
References
编辑手记