Distribution of periodic points of polynomial diffeomorphisms of C^2

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 $\mu$ 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 $f$.

References in corpus (1)

• Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents

Cited by in corpus (3)

• Bers and Hénon, Painlevé and Schroedinger
• Growth of the number of periodic points for meromorphic maps
• Hölder continuity and laminarity of the Green currents for Hénon-like maps