Characterization of Dynamics of a Class of Polynomial Automorphisms in ℂn

Abstract

A kind of higher-dimensional complex polynomial mappings [Formula: see text] is considered: [Formula: see text] where [Formula: see text], [Formula: see text] are polynomials with degrees higher than one, and [Formula: see text] are nonzero complex numbers, [Formula: see text]. Assume that each [Formula: see text] is hyperbolic on its Julia set and [Formula: see text] is sufficiently small, [Formula: see text], then there exists a bounded set on which the dynamics on the forward and backwards Julia sets are described by using the inductive and the projective limits, respectively. These results are a natural higher-dimensional generalization of the work of Hubbard and Oberste-Vorth on two-dimensional complex Hénon mappings. The combination of the symbolic dynamics and the crossed mapping is also applied to study the complicated dynamics of a class of polynomial mappings in [Formula: see text].