Equivalent conditions for hyperbolicity on partially hyperbolic holomorphic maps

Francisco Valenzuela-Henríquez

doi:10.1512/iumj.2011.60.4375

Equivalent conditions for hyperbolicity on partially hyperbolic holomorphic maps

Francisco Valenzuela-Henríquez

INSTITUTE OF MATHEMATICS

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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 language	English
Pages (from-to)	1363-1392
Number of pages	30
Journal	Indiana University Mathematics Journal
Volume	60
Issue number	4
DOIs	https://doi.org/10.1512/iumj.2011.60.4375
State	Published - 2011

Keywords

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

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10.1512/iumj.2011.60.4375

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AB - 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.

KW - 32A10

KW - 37D30

KW - Holomorphic functions. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 37D10

KW - Invariant manifold theory

KW - Partially hyperbolic systems and dominated splittings

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VL - 60

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EP - 1392

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

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ER -

Equivalent conditions for hyperbolicity on partially hyperbolic holomorphic maps

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Keywords

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