Uniqueness of the measure of maximal entropy for the squarefree flow

Ryan Peckner

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arXiv · 1205.2905

Uniqueness of the measure of maximal entropy for the squarefree flow

Ryan Peckner

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Abstract

The squarefree flow is a natural dynamical system whose topological and ergodic properties are closely linked to the behavior of squarefree numbers. We prove that the squarefree flow carries a unique measure of maximal entropy and express this measure explicitly in terms of a skew-product of a Kronecker and a Bernoulli system. Using this characterization and a number-theoretic argument, we then show that the unique maximum entropy measure fails to possess the Gibbs property.

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Ryan Peckner. 2014-10-07. Uniqueness of the measure of maximal entropy for the squarefree flow. https://arxiv.org/abs/1205.2905

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