On amenable semigroups of rational functions

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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.

Original languageAmerican English
Pages (from-to)7945-7979
Number of pages35
JournalTransactions of the American Mathematical Society
Issue number11
StatePublished - 1 Nov 2022


  • math.CV
  • math.DS

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • General Mathematics


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