2002/07/22 by Rasul Shafikov, Christian Wolf, Shafikov, Rasul +1
Mathematics · #32H50 #37C45 #37FXX #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.CV #math.DS #msc:32H50 #msc:37C45 #msc:37FXX
paper · pdf · doi:10.48550/arxiv.math/0207190
19 pages
arxiv created 2002/07/22 · openalex publication_date 2002/07/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the dynamics of regular polynomial automorphisms of Cn. These maps provide a natural generalization of complex Henon maps in C2 to higher dimensions. For a given regular polynomial automorphism f we construct a filtration in Cn which has particular escape properties for the orbits of f. In the case when f is hyperbolic we obtain a complete description of its orbits. In the second part of the paper we study the Hausdorff and box dimension of the Julia sets of f. We show that the Julia set J has positive box dimension, and (provided f is not volume preserving) that the filled-in Julia set K has box dimension strictly less than 2n. Moreover, if f is hyperbolic, then the Hausdorff dimension of the forward/backward Julia set J+/- is strictly less than 2n.