Dynamical properties of the Pascal adic transformation

Xavier Mela; Karl Petersen

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Dynamical properties of the Pascal adic transformation

Xavier Mela·Karl Petersen

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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.

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BibTeX RIS

Xavier Mela, Karl Petersen. 2003-10-20. Dynamical properties of the Pascal adic transformation. https://arxiv.org/abs/math/0310317

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