2021/03/18 by Jason P. Bell, Keping Huang, Bell, Jason P. +5 · 1 citation
Computer Science · Mathematics · #20D15 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Primary: 20M05. Secondary: 14H37 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2103.09994
openalex publication_date 2021/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an analog of the Tits alternative for rational functions. In particular, we show that if S is a finitely generated semigroup of rational functions over the complex numbers, then either S has polynomially bounded growth or S contains a nonabelian free semigroup. We also show that if f and g are polarizable maps over any field that do not have the same set of preperiodic points, then the semigroup generated by f and g contains a nonabelian free semigroup.