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Dynamics of hyperbolic correspondences
Part of:
Complex dynamical systems
Published online by Cambridge University Press: 04 May 2021
Abstract
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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.
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