标题：Characterization of Dynamics of a Class of Polynomial Automorphisms in C-n
作者机构：[Zhang, Xu] Shandong Univ, Dept Math, Weihai 264009, Shandong, Peoples R China.
通讯作者地址：[Zhang, X]Shandong Univ, Dept Math, Weihai 264009, Shandong, Peoples R China.
来源：INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
关键词：Backwards Julia set; crossed mapping; forward Julia set; hyperbolic;; inductive limit; projective limit
摘要：A kind of higher-dimensional complex polynomial mappings F : C-n -> C-n is considered:; [GRAPHICS]; ,; where z = (z(1), ..., Z(n)) is an element of C-n, p(i) are polynomials with degrees higher than one, and alpha(i) are nonzero complex numbers, 1 <= i <= n - 1. Assume that each p(i) is hyperbolic on its Julia set and vertical bar alpha(i)vertical bar is sufficiently small, 1 <= i <= n - 1, 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 Henon 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 C-3.