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Celestial encounters. The origins of chaos and stability. (English) Zbl 0944.37001

Princeton, NJ: Princeton University Press. 233 p. (1996).
The book emerged as a happy outcome of the cooperation of two scientists specialized in celestial mechanics and dynamical systems driven by the same urge to diffuse knowledge about the theory of chaos and redefine its origins.
The book is addressed to the general public with the exception of specific subjects for which formalization and proper definitions are unavoidable. The scientific issues presented in each chapter are related to the relevant historical encounters and the personalities of the scientists stimulating the interest of the readers.
The geometrical approach to the study of differential equations and the notion of phase space as founded by Poincaré occupy the first two chapters. Theory of singularities and collisions are presented in the third chapter and the notion of stability is presented in its historic perspective in the fourth chapter. The link of chaos and stability to the mathematical models of universe is revealed through the presentation of KAM theory in the fifth chapter.

MSC:

37-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory
70-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems
70F15 Celestial mechanics
01A05 General histories, source books
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C75 Stability theory for smooth dynamical systems
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