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arXiv · 2109.11601

On amenability and measure of maximal entropy for semigroups of rational maps: II

Peter Makienko·Carlos Cabrera
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Abstract

We compare dynamical and algebraic properties of semigroups of rational maps. In particular, we show a version of the Day-von Neumann's conjecture and give a partial positive answer to "Sushkievich's problem" for semigroups of rational maps. We also show the relation of these conjectures with Furstenberg's $\times 2 \times 3$ problem and prove a coarse version of Furstenberg's problem for semigroups of non-exceptional polynomials.

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Peter Makienko, Carlos Cabrera. 2021-09-23. On amenability and measure of maximal entropy for semigroups of rational maps: II. https://arxiv.org/abs/2109.11601

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