Hyperbolic polynomial diffeomorphisms of C2. II: Hubbard trees

    研究成果: ジャーナルへの寄稿学術誌査読

    7 被引用数 (Scopus)

    抄録

    This paper is a sequel to Part I [Y. Ishii, Hyperbolic polynomial diffeomorphisms of C2. I: A non-planar map, Adv. Math. 218 (2) (2008) 417-464]. In the current article we construct an object analogous to a Hubbard tree consisting of a pair of trees decorated with loops and a pair of maps between them for a hyperbolic polynomial diffeomorphism f of C2. Key notions in the construction are the pinching disks and the pinching locus which determine how local dynamical pieces are glued together to obtain a global picture. It is proved that the shift map on the orbit space of a Hubbard tree is topologically conjugate to f on its Julia set. Several examples of Hubbard trees are also given.

    本文言語英語
    ページ(範囲)985-1022
    ページ数38
    ジャーナルAdvances in Mathematics
    220
    4
    DOI
    出版ステータス出版済み - 3月 1 2009

    !!!All Science Journal Classification (ASJC) codes

    • 数学一般

    フィンガープリント

    「Hyperbolic polynomial diffeomorphisms of C2. II: Hubbard trees」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

    引用スタイル