Ergodic Theory of Numbers, Volume 29

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Cambridge University Press, Sep 12, 2002 - Mathematics - 190 pages
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This book is an introduction to the ergodic theory behind common number expansions, for instance decimal expansions, continued fractions and many others. The questions studied are dynamical as well as number theoretic in nature, and the answers are obtained with the help of ergodic theory. What it means to be ergodic and the basic ideas behind ergodic theory are explained along the way. The book is aimed at introducing students with sufficient background knowledge in real analysis to a 'dynamical way of thinking'. The subjects covered vary from the classical to recent research which should increase the appeal of this book to researchers working in the field.
 

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Contents

Variations on a theme Other expansions
33
Ergodicity
57
Systems obtained from other systems
89
Diophantine approximation and continued fractions
115
Entropy
155
Bibliography
179
Index
187
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