Ergodic theory of numbers / Karma Dajani, Cor Kraaikamp.

Format:

Book

Author/Creator:

Dajani, Karma, author.

Kraaikamp, Cor, author.

Series:

Carus mathematical monographs ; Number 29.

Carus Mathematical Monographs ; Number 29

Language:

English

Subjects (All):

Ergodic theory.

Physical Description:

1 online resource (x, 190 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington : Mathematical Association of America, 2002.

Language Note:

English

Summary:

Ergodic Theory of Numbers 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:

Variations on a theme

Ergodicity

Systems obtained from other systems

Diophantine approximation and continued fractions

Entropy.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-61444-027-1