Sharing a measure of maximal entropy in polynomial semigroups

Fedor Pakovich

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arXiv · 2009.12261

Sharing a measure of maximal entropy in polynomial semigroups

Fedor Pakovich

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Abstract

Let $P_1,P_2,\dots, P_k$ be complex polynomials of degree at least two that are not simultaneously conjugate to monomials or to Chebyshev polynomials, and $S$ the semigroup under composition generated by $P_1,P_2,\dots, P_k$. We show that all elements of $S$ share a measure of maximal entropy if and only if the intersection of principal right ideals $SP_1\cap SP_2\cap \dots \cap SP_k$ is non-empty.

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Fedor Pakovich. 2020-09-25. Sharing a measure of maximal entropy in polynomial semigroups. https://arxiv.org/abs/2009.12261

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