## Abstract

This paper is a sequel to Part I [Y. Ishii, Hyperbolic polynomial diffeomorphisms of C^{2}. 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 C^{2}. 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 language | English |
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Pages (from-to) | 985-1022 |

Number of pages | 38 |

Journal | Advances in Mathematics |

Volume | 220 |

Issue number | 4 |

DOIs | |

Publication status | Published - Mar 1 2009 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

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