## Institute for Mathematical Sciences

## Preprint ims93-1

** E. Bedford, M. Lyubich, and J. Smillie**
* Distribution of Periodic Points of Polynomial Diffeomorphisms of C^2*

Abstract: (under construction) 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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