A non-archimedean $\lambda$-lemma
Dynamical Systems
2018-11-01 v3 Number Theory
Abstract
We provide a framework for studying the dynamics of families of one-variable rational functions parametrized by Berkovich spaces over a complete non-archimedean field. We prove a non-archimedean analogue of Ma\~{n}\'{e}, Sad, and Sullivan's -Lemma and use this to show an equivalence of two stability conditions for families of rational functions parametrized by an open subset of the Berkovich affine line.
Cite
@article{arxiv.1712.01372,
title = {A non-archimedean $\lambda$-lemma},
author = {Thomas Silverman},
journal= {arXiv preprint arXiv:1712.01372},
year = {2018}
}