Attractors associated to a family of hyperbolic $p$-adic plane automorphisms
Dynamical Systems
2020-01-27 v3 Number Theory
Abstract
We consider a certain two-parameter family of automorphisms of the affine plane over a complete, locally compact non-Archimedean field. Each of these automorphisms admits a chaotic attractor on which it is topologically conjugate to a full two-sided shift map, and the attractor supports a unit Borel measure which describes the distribution of the forward orbit of Haar-almost all points in the basin of attraction. We also compute the Hausdorff dimension of the attractor, which is non-integral.
Keywords
Cite
@article{arxiv.1810.06708,
title = {Attractors associated to a family of hyperbolic $p$-adic plane automorphisms},
author = {Clayton Petsche},
journal= {arXiv preprint arXiv:1810.06708},
year = {2020}
}