Ergodic Theory of Numbers

Karma Dajani, Cor Kraaikamp

190 pages, parution le 17/03/2003

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Résumé

This book is an introduction to the ergodic theory behind common number expansion, like decimal expansions, continued fractions, and many others. However, its aim does not stop there. For undergraduate students with sufficient background knowledge in real analysis and graduate students interested in the area, it is also an introduction to a “dynamical way of thinking.” The questions studied here are dynamical as well as number theoretical in nature, and the answers are obtained with the help of ergodic theory. Attention is focused on concepts like measure-preserving, ergodicity, natural extension, induced transformations, and entropy. These concepts are then applied to familiar expansions to obtain old and new results in an elegant and straightforward manner. What it means to be ergodic and the basic ideas behind ergodic theory will be explained along the way. The subjects covered vary from classical to recent, which makes this book appealing to researchers as well as students.

Contents

Introduction
Variations on a theme (other expansions)
Ergodicity
Systems obtained from other systems
Diophantine approximation and continued fractions
Entropy

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Karma Dajani, Cor Kraaikamp
Parution	17/03/2003
Nb. de pages	190
Format	14,5 x 21,5
Couverture	Relié
Poids	350g
Intérieur	Noir et Blanc
EAN13	9780883850343
ISBN13	978-0-88385-034-3