On amenable semigroups of rational functions-Reference-Cited by-同舟云学术

On amenable semigroups of rational functions

Published:2022-09-02 Issue:11 Volume:375 Page:7945-7979
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Pakovich Fedor

Abstract

We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation. We also prove a number of results about amenable semigroups of arbitrary rational functions. In particular, we show that under quite general conditions a semigroup of rational functions is amenable if and only if it is a subsemigroup of the centralizer of some rational function.

Funder

Israel Science Foundation

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/tran/2022-375-11/S0002-9947-2022-08731-6/tran8731_AM.pdf

Reference47 articles.

1. Commuting polynomials and polynomials with same Julia set;Atela, Pau;Internat. J. Bifur. Chaos Appl. Sci. Engrg.,1996

2. Semigroups satisfying a strong Følner condition;Argabright, L. N.;Proc. Amer. Math. Soc.,1967

3. A problem on Julia sets;Baker, I. N.;Ann. Acad. Sci. Fenn. Ser. A I Math.,1987

4. Symmetries of Julia sets;Beardon, A. F.;Bull. London Math. Soc.,1990

5. Graduate Texts in Mathematics;Beardon, Alan F.,1991

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A Tits alternative for endomorphisms of the projective line;Journal of the European Mathematical Society;2023-10-31

2. Irreducible polynomials in quadratic semigroups;Journal of Number Theory;2023-07