On amenable semigroups of rational functions

DOI10.1090/tran/8731OpenAlexW3081346759WikidataQ113822433 ScholiaQ113822433MaRDI QIDQ5039727

Fedor Pakovitch

Publication date: 4 October 2022

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.12194

zbMATH Keywords

semigroupspolynomialsrational functionsamenability

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Polynomials in general fields (irreducibility, etc.) (12E05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (3)

On amenability and measure of maximal entropy for semigroups of rational maps: II ⋮ Irreducible polynomials in quadratic semigroups ⋮ When do two rational functions have locally biholomorphic Julia sets?

Cites Work

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• Linear relations between polynomial orbits
• Rational functions with identical measure of maximal entropy
• Amenable semigroups
• On rational functions sharing the measure of maximal entropy
• Semidirect product of semigroups in relation to amenability, cancellation properties, and strong Folner conditions
• Amenability and measure of maximal entropy for semigroups of rational maps
• On polynomials sharing preimages of compact sets, and related questions
• Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture
• Symmetries on the Julia set
• The Banach–Tarski Paradox
• COMMUTING POLYNOMIALS AND POLYNOMIALS WITH SAME JULIA SET
• Polynomial semiconjugacies, decompositions of iterations, and invariant curves
• Algebraic curvesP(x) −Q(y) = 0 and functional equations
• Symmetries of Julia Sets
• An invariant measure for rational maps
• A problem of Julia sets
• Poiynomials with identical Julia sets
• When do two rational functions have the same Julia set?
• Ensembles d'unicité pour les polynômes
• The Polynomials Associated with a Julia Set
• Amenability of Discrete Groups by Examples
• Algebraic curves $A^{\circ l}(x)-U(y)=0$ and arithmetic of orbits of rational functions
• Finiteness theorems for commuting and semiconjugate rational functions
• Commuting rational functions revisited
• Powers in Orbits of Rational Functions: Cases of an Arithmetic Dynamical Mordell–Lang Conjecture
• Distribution des préimages et des points périodiques d’une correspondance polynomiale
• Amenability and geometry of semigroups
• Folner's Conditions for Amenable Semi-Groups.
• Semigroups Satisfying a Strong Folner Condition
• Polynomial Substitutions
• Means for the Bounded Functions and Ergodicity of the Bounded Representations of Semi-Groups
• Tame rational functions: decompositions of iterates and orbit intersections

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