Distribution of periodic points of polynomial diffeomorphisms of C^2

Details Distribution of periodic points of polynomial diffeomorphisms of C^2 Distribution of periodic points of polynomial diffeomorphisms of C^2

1993-01-23

arxiv.org/abs/math/9301220v1

Mathematics

Dynamical Systems

Scientific paper

10.1007/BF01232671

This paper deals with the dynamics of a simple family of holomorphic diffeomorphisms of $\C^2$: 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 $\mu$ of the set $K$ of points with bounded orbits. In [BLS] $\mu$ is also characterized dynamically as the unique measure of maximal entropy. Thus $\mu$ is also an equilibrium measure from the point of view of the thermodynamical formalism. In the present paper we give another dynamical interpretation of $\mu$ as the limit distribution of the periodic points of $f$.

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