Dynamics of (Pseudo) Automorphisms of 3-space: Periodicity versus positive entropy
Dynamical Systems
2012-06-12 v3 Algebraic Geometry
Complex Variables
Abstract
We study the iterative behavior of the family of 3-step linear fractional recurrences and the family of birational maps they define. We determine all the possible periodicities within this family or, equivalently, the birational maps of finite order. This family also contains pseudo-automorphisms of infinite order. One such family consists of completely integrable maps, and another family consists of maps of positive entropy. Both of these families have invariant families of surfaces.
Keywords
Cite
@article{arxiv.1101.1614,
title = {Dynamics of (Pseudo) Automorphisms of 3-space: Periodicity versus positive entropy},
author = {Eric Bedford and Kyounghee Kim},
journal= {arXiv preprint arXiv:1101.1614},
year = {2012}
}