Dynamical compactifications of $\mathbf{C}^2$

Abstract

We find good dynamical compactifications for arbitrary polynomial mappings of $\mathbf{C}^2$ and use them to show that the degree growth sequence satisfies a linear integral recursion formula. For maps of low topological degree we prove that the Green function is well behaved. For maps of maximum topological degree, we give normal forms.

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Authors

Charles Favre

CNRS-Université Paris 7
Institut de Mathématiques
F-75251 Paris
France

Current address:

Centre de Mathématiques Laurent-Schwartz
École Polytechnique
91128 Palaiseau Cedex
France Mattias Jonsson

Department of Mathematics
University of Michigan
Ann Arbor, MI 48109-1043