Jason P. Bell, Keping Huang, Wayne Peng, Thomas J. Tucker
Published 2021-03-18Version 1
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.
On preperiodic points of rational functions defined over $\mathbb{F}_p(t)$
Portraits of preperiodic points for rational maps
Reducibility of rational functions in several variables
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