标题：Characterization of Dynamics of a Class of Polynomial Automorphisms in Cn
作者机构：[Zhang, Xu ] Department of Mathematics, Shandong University, Shandong, Weihai; 264209, China
来源：International Journal of Bifurcation and Chaos
摘要：A kind of higher-dimensional complex polynomial mappings F: Cn → Cn is considered: [Equation presented here], where z = (z1,&mellip;,zn) ∈ Cn, pi are polynomials with degrees higher than one, and αi are nonzero complex numbers, 1 ≤ i ≤ n - 1. Assume that each pi is hyperbolic on its Julia set and |αi| 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 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 C3.
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