Sharing a Measure of Maximal Entropy in Polynomial Semigroups

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Let \P1,P2,\ Pk\ 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 \P1,P2,\ Pk\. We show that all elements of \S\ share a measure of maximal entropy if and only if the intersection of principal left ideals \SP1\cap SP2\cap \dots \cap SPk\ is non-empty.
Original languageEnglish GB
JournalInternational Mathematics Research Notices
Issue numberrnab076
StatePublished - 1 May 2021


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