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Dynamics of hyperbolic correspondences

Part of: Complex dynamical systems

Published online by Cambridge University Press:  04 May 2021

CARLOS SIQUEIRA Open the ORCID record for CARLOS SIQUEIRA [Opens in a new window]
CARLOS SIQUEIRA*
Affiliation:
Department of Mathematics, Federal University of Bahia, SalvadorCEP 40170115, Brazil
*
e-mail: [email protected]
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Abstract

This paper establishes the geometric rigidity of certain holomorphic correspondences in the family $(w-c)^q=z^p$ , whose post-critical set is finite in any bounded domain of $\mathbb {C}$ . In spite of being rigid on the sphere, such correspondences are J-stable by means of holomorphic motions when viewed as maps of $\mathbb {C}^2$ . The key idea is the association of a conformal iterated function system to the return branches near the critical point, giving a global description of the post-critical set and proving the hyperbolicity of these correspondences.

Keywords

complex dynamicsholomorphic correspondencesrigidity

MSC classification

Primary: 37F15: Expanding maps; hyperbolicity; structural stability 37F05: Relations and correspondences
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 8 , August 2022 , pp. 2661 - 2692
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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