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arXiv · 2103.09994

A Tits alternative for rational functions

Jason P. Bell·Keping Huang·Wayne Peng·Thomas J. Tucker
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Abstract

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.

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Jason P. Bell, Keping Huang, Wayne Peng, Thomas J. Tucker. 2021-03-18. A Tits alternative for rational functions. https://arxiv.org/abs/2103.09994

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