Dynamics of hyperbolic correspondences

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...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2022-08, Vol.42 (8), p.2661-2692
Main Author: SIQUEIRA, CARLOS
Format: Article
Language:English
Subjects:
Correspondence
Critical point
Mathematical analysis
Orbits
Original Article
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Summary: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2021.49