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Sharing a Measure of Maximal Entropy in Polynomial Semigroups
International Mathematics Research Notices ( IF 0.9 ) Pub Date : 2021-03-10 , DOI: 10.1093/imrn/rnab076
Fedor Pakovich 1
Affiliation  

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 left ideals $SP_1\cap SP_2\cap \dots \cap SP_k$ is non-empty.

中文翻译:

共享多项式半群中的最大熵测度

令 $P_1,P_2,\dots , P_k$ 是至少二次的复多项式,它们不同时与单项式或切比雪夫多项式共轭,$S$ 是由 $P_1,P_2,\dots , P_k 生成的合成下的半群美元。我们证明,当且仅当主左理想的交集 $SP_1\cap SP_2\cap \dots\cap SP_k$ 非空时,$S$ 的所有元素共享一个最大熵度量。
更新日期:2021-03-10
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