Dynamical Systems I - D. V. Anosov

. .

Résumé :
From the reviews: The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book. Journal de Physique

Sommaire:
Ordinary Differential Equations.- Preface.- Basic Concepts.- Differential Equations on Surfaces.- Singular Points of Differential Equations in Higher Dimensional Real Phase Space.- Singular Points of Differential Equations in Higher Dimensional Complex Phase Space.- Singular Points of Vector Fields in the Real and Complex Planes.- Cycles.- Analytic Theory of Differential Equations.- Smooth Dynamical Systems.- Preface.- Basic Concepts.- Elementary Theory.- Topological Dynamics.- Flows on Two-Dimensional Manifolds.

From the reviews: The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book. Journal de Physique