Number Theory and Dynamical Systems

Front Cover
M. M. Dodson, J. A. G. Vickers, N. J. Hitchin
Cambridge University Press, Nov 9, 1989 - Mathematics - 172 pages
This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems.
 

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Contents

Introduction
1
Chapter2
19
Chapter3 87
37
Chapter4
49
Chapter5
69
Chapter6
87
Chapter7
103
Chapter8
117
Chapter9 _
137
Chapter 10
153
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