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Dynamical properties of the Pascal adic transformation

Published online by Cambridge University Press:  22 December 2004

XAVIER MÉLA  and
KARL PETERSEN
XAVIER MÉLA
Affiliation:
IML, 163 avenue de Luminy, Case 907, 13288 Marseille Cedex 09, France (e-mail: mela@iml.univ-mrs.fr)
KARL PETERSEN
Affiliation:
Department of Mathematics, CB 3250 Phillips Hall, University of North Carolina, Chapel Hill, NC 27599, USA (e-mail: petersen@math.unc.edu)
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Abstract

We study the dynamics of a transformation that acts on infinite paths in the graph associated with Pascal's triangle. For each ergodic invariant measure the asymptotic law of the return time to cylinders is given by a step function. We construct a representation of the system by a subshift on a two-symbol alphabet and then prove that the complexity function of this subshift is asymptotic to a cubic, the frequencies of occurrence of blocks behave in a regular manner, and the subshift is topologically weak mixing.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 1 , February 2005 , pp. 227 - 256
Copyright
2005 Cambridge University Press

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