Equivalent conditions for hyperbolicity on partially hyperbolic holomorphic maps

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Abstract

Let f : Cn → Cn, with n ≥ 2, be a biholomorphism, and let Cn be a compact f -invariant set such that f |? is partially hyperbolic. We give equivalent conditions for hyperbolicity on ?. In particular, for generalized Hènon maps with dominated splitting in the Julia set J, we characterize the hyperbolicity of J.

Original languageEnglish
Pages (from-to)1363-1392
Number of pages30
JournalIndiana University Mathematics Journal
Volume60
Issue number4
DOIs
StatePublished - 2011
Externally publishedYes

Keywords

  • 32A10
  • 37D30
  • Holomorphic functions. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 37D10
  • Invariant manifold theory
  • Partially hyperbolic systems and dominated splittings

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