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Affine actions of a free semigroup on the real line

Published online by Cambridge University Press:  11 September 2006

VITALY BERGELSON ,
MICHAŁ MISIUREWICZ  and
SAMUEL SENTI
VITALY BERGELSON
Affiliation:
Department of Mathematics, Ohio State University, Columbus, OH 43210, USA (e-mail: [email protected])
MICHAŁ MISIUREWICZ
Affiliation:
Department of Mathematical Sciences, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202-3216, USA (e-mail: [email protected])
SAMUEL SENTI
Affiliation:
Instituto de Matematica Pura e Aplicada, Rio de Janeiro 22460-320, Brazil (e-mail: [email protected])
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Abstract

We consider actions of the free semigroup with two generators on the real line, where the generators act as affine maps, one contracting and one expanding, with distinct fixed points. Then every orbit is dense in a half-line, which leads to the question whether it is, in some sense, uniformly distributed. We present answers to this question for various interpretations of the phrase ‘uniformly distributed’.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 5 , October 2006 , pp. 1285 - 1305
Copyright
2006 Cambridge University Press

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