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Distribution of periodic points of polynomial diffeomorphisms of C^2

Eric Bedford·Mikhail Lyubich·John Smillie
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Abstract

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 $μ$ of the set $K$ of points with bounded orbits. In [BLS] $μ$ is also characterized dynamically as the unique measure of maximal entropy. Thus $μ$ is also an equilibrium measure from the point of view of the thermodynamical formalism. In the present paper we give another dynamical interpretation of $μ$ as the limit distribution of the periodic points of $f$.

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Eric Bedford, Mikhail Lyubich, John Smillie. 1993-01-23. Distribution of periodic points of polynomial diffeomorphisms of C^2. https://doi.org/10.1007/bf01232671

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