A uniform Tits alternative for endomorphisms of the projective line
Number Theory
2025-04-22 v1 Dynamical Systems
Group Theory
Abstract
A recent article of J.P. Bell, K. Huang, W. Peng and T.J. Tucker establishes an analog of the Tits alternative for semigroups of endomorphisms of the projective line. The proof involves a ping-pong argument on arithmetic height functions. Extending this method, we obtain a uniform version of the same alternative. In particular, we show that semigroups of of exponential growth are of uniform exponential growth.
Cite
@article{arxiv.2504.14263,
title = {A uniform Tits alternative for endomorphisms of the projective line},
author = {Alonso Beaumont},
journal= {arXiv preprint arXiv:2504.14263},
year = {2025}
}