Dynamical properties of the Pascal adic transformation

By Xavier Méla, K. Petersen. Ergodic Theory and Dynamical Systems, 2003

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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.

Subfields: Computational Theory and Mathematics, Mathematical Physics

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