Ergodic properties of signed binary expansions

Karma Dajani; Cor Kraaikamp; Pierre Liardet

doi:10.3934/dcds.2006.15.87

Article Contents

2006, Volume 15, Issue 1: 87-119. Doi: 10.3934/dcds.2006.15.87

This issue Previous Article Multiple stable patterns for some reaction-diffusion equation in disrupted environments Next Article Behaviors of solutions to a scalar-field equation involving the critical Sobolev exponent with the Robin condition

Ergodic properties of signed binary expansions

1.
Universiteit Utrecht, Fac. Wiskunde en Informatica and MRI, Budapestlaan 6, P.O. Box 80.000, 3508 TA Utrecht
2.
Technische Universiteit Delft, EWI, Thomas Stieltjes Institute for Mathematics, Mekelweg 4, 2628 CD Delft
3.
Université de Provence, Centre de Mathématiques et Informatique, 39 rue Joliot-Curie, F-13453 Marseille cedex 13

Received: September 2005

Revised: December 2005

Published: February 2006

Abstract / Introduction Related Papers Cited by

Abstract

In this paper it is shown that the classical signed binary expansion involves mainly two dynamical systems: the binary odometer and a three state Markov chain. Introducing the notions of additive and multiplicative block functions (e.g., sum-of-digits and Hamming weight functions), we derive dynamical systems which are skew products over the odometer. Their spectral properties are investigated, and applications are given to certain Maharam extensions. The proofs are related to the spectral measure of unitary operators, obtained from cocycles associated to block functions.

Keywords:

Mathematics Subject Classification: 37Axx, 11K55.

Citation:

Article Metrics

HTML views() PDF downloads(139) Cited by(0)

Ergodic properties of signed binary expansions

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Ergodic properties of signed binary expansions

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content