Dynamics of Polynomial Diffeomorphisms of C2: Combinatorial and Topological Aspects

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    2 Citations (Scopus)

    Abstract

    The Fig. 1 was drawn by Shigehiro Ushiki using his software called HenonExplorer. This complicated object is the Julia set of a complex Hénon map fc , b(x, y) = (x2+ c- by, x) defined on C2 together with its stable and unstable manifolds, hence it is a fractal set in the real 4-dimensional space! The purpose of this paper is to survey some results, questions and problems on the dynamics of polynomial diffeomorphisms of C2 including complex Hénon maps with an emphasis on the combinatorial and topological aspects of their Julia sets.

    Original languageEnglish
    Pages (from-to)119-173
    Number of pages55
    JournalArnold Mathematical Journal
    Volume3
    Issue number1
    DOIs
    Publication statusPublished - Apr 1 2017

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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