Minimally critical regular endomorphisms of A^N
Dynamical Systems
2021-03-08 v2 Number Theory
Abstract
We study the dynamics of a class of endomorphisms of A^N which restricts, when N = 1, to the class of unicritical polynomials. Over the complex numbers, we obtain lower bounds on the sum of Lyapunov exponents, and a statement which generalizes the compactness of the Mandelbrot set. Over the algebraic numbers, we obtain estimates on the critical height, and over general algebraically closed fields we obtain some rigidity results for post-critically finite morphisms of this form.
Cite
@article{arxiv.2006.15365,
title = {Minimally critical regular endomorphisms of A^N},
author = {Patrick Ingram},
journal= {arXiv preprint arXiv:2006.15365},
year = {2021}
}