Hyperbolic polynomial diffeomorphisms of C2. II: Hubbard trees

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7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)985-1022
Number of pages38
JournalAdvances in Mathematics
Volume220
Issue number4
DOIs
Publication statusPublished - Mar 1 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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