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Professor Liao Shantao is an outstanding mathematician in China. As a result of his profound and systematic research work, he won the Mathematics Prize in 1985 which was the first time awarded by the Third World Academy of Sciences for his contributions to differentiable dynamical systems and other fields. He also won first-class award of National Natural Science Prize of China in 1987, The Chinese edition of this book collects eight of his major articles on differentiable dynamical systems in the period of 1963 - 1984, arranged in the order according to the dates of submission for publications, together with a preface and an appendix written also by him. Other two appendices A and B, which are original articles by Liao, are added to the translation to the English edition. .
This book introduces systematically the derivation of the two fundamental notions of "standard systems of differential equations" and "obstruction sets" and exhibits their important properties and applications to stability problems.

Preface to the English Edition 
Preface to the Chinese Edition 
Chapter 1 Certain Ergodic Properties of a Differential System 
on a Compact Differentiable Manifold 
1.1 One-parameter Transformation Group..

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