Sharing a Measure of Maximal Entropy in Polynomial Semigroups

Fedor Pakovich

doi:10.1093/imrn/rnab076

Sharing a Measure of Maximal Entropy in Polynomial Semigroups

Fedor Pakovich

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

Let P₁, P₂, . . . , 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 P₁, P₂, . . . , P_k. We show that all elements of S share a measure of maximal entropy if and only if the intersection of principal left ideals SP₁ ∩ SP₂ ∩ · · · ∩ SP_k is non-empty.

Original language	American English
Pages (from-to)	13829-13840
Number of pages	12
Journal	International Mathematics Research Notices
Volume	2022
Issue number	18
DOIs	https://doi.org/10.1093/imrn/rnab076
State	Published - 1 Sep 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnab076

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abstract = "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 ∩ SP2 ∩ · · · ∩ SPk is non-empty.",

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Sharing a Measure of Maximal Entropy in Polynomial Semigroups

Abstract

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