多项式半群的最大熵分担测度
Sharing a measure of maximal entropy in polynomial semigroups
摘要：
设$P_1,P_2,\dots, P_k$是至少二次的复多项式，且不同时共轭于单项式或切比雪夫多项式，$S$是由$P_1,P_2,\dots, P_k$生成的复合半群.我们证明了$S$的所有元素共享一个最大熵测度当且仅当主右理想$SP_1\cap SP_2\cap \dots \cap SP_k$的交集非空.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
