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Bibliographic Details
Main Author: Laude, Miguel Ratis
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2411.08748
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author Laude, Miguel Ratis
author_facet Laude, Miguel Ratis
contents In recent years, the study of holomorphic correspondences as dynamical systems that can display behaviors of both rational maps and Kleinian groups has gained a good amount of attention. This phenomenon is related to the Sullivan dictionary, a list of parallels between the theories of these two systems. We build upon a surgical construction of such matings, due to Bullett and Harvey, increasing the degree of maps we consider, and proving regularity properties of the mating map on parameter spaces: namely, analyticity on the interior of its domain of definition, and continuity under quasiconformal rigidity on the boundary.
format Preprint
id arxiv_https___arxiv_org_abs_2411_08748
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Continuity of matings of Kleinian groups and polynomials
Laude, Miguel Ratis
Dynamical Systems
In recent years, the study of holomorphic correspondences as dynamical systems that can display behaviors of both rational maps and Kleinian groups has gained a good amount of attention. This phenomenon is related to the Sullivan dictionary, a list of parallels between the theories of these two systems. We build upon a surgical construction of such matings, due to Bullett and Harvey, increasing the degree of maps we consider, and proving regularity properties of the mating map on parameter spaces: namely, analyticity on the interior of its domain of definition, and continuity under quasiconformal rigidity on the boundary.
title Continuity of matings of Kleinian groups and polynomials
topic Dynamical Systems
url https://arxiv.org/abs/2411.08748