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Dynamics of hyperbolic correspondences
Part of:
Complex dynamical systems
Published online by Cambridge University Press: 04 May 2021
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.
MSC classification
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
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