Distribution of periodic points of polynomial diffeomorphisms of C^2
Dynamical Systems
2016-09-06 v1
Abstract
This paper deals with the dynamics of a simple family of holomorphic diffeomorphisms of : the polynomial automorphisms. This family of maps has been studied by a number of authors. We refer to [BLS] for a general introduction to this class of dynamical systems. An interesting object from the point of view of potential theory is the equilibrium measure of the set of points with bounded orbits. In [BLS] is also characterized dynamically as the unique measure of maximal entropy. Thus is also an equilibrium measure from the point of view of the thermodynamical formalism. In the present paper we give another dynamical interpretation of as the limit distribution of the periodic points of .
Keywords
Cite
@article{arxiv.math/9301220,
title = {Distribution of periodic points of polynomial diffeomorphisms of C^2},
author = {Eric Bedford and Mikhail Lyubich and John Smillie},
journal= {arXiv preprint arXiv:math/9301220},
year = {2016}
}