English

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 \C2\C^2: 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 μ\mu of the set KK of points with bounded orbits. In [BLS] μ\mu is also characterized dynamically as the unique measure of maximal entropy. Thus μ\mu is also an equilibrium measure from the point of view of the thermodynamical formalism. In the present paper we give another dynamical interpretation of μ\mu as the limit distribution of the periodic points of ff.

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}
}