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

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arxiv 2109.11601 v5 pith:PI7ZL2DT submitted 2021-09-23 math.DS math.CV

Peter Makienko , Carlos Cabrera This is my paper · ORCID
classification math.DSmath.CV
keywords semigroupsmapsproblemrationalfurstenbergtimesversionalgebraic
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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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