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On quasiconformal non-equivalence of gasket Julia sets and limit sets

Part of: Geometric function theory Complex dynamical systems

Published online by Cambridge University Press:  09 June 2025

YUSHENG LUO Open the ORCID record for YUSHENG LUO [Opens in a new window]  and
YONGQUAN ZHANG Open the ORCID record for YONGQUAN ZHANG [Opens in a new window]
YUSHENG LUO
Affiliation:
Department of Mathematics, https://ror.org/05bnh6r87Cornell University, 212 Garden Ave, Ithaca, NY 14853, USA (e-mail: yusheng.s.luo@gmail.com)
YONGQUAN ZHANG*
Affiliation:
Institute for Mathematical Sciences, https://ror.org/05qghxh33Stony Brook University, 100 Nicolls Rd, Stony Brook, NY 11794-3660, USA
*
e-mail: yqzhangmath@gmail.com
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Abstract

This paper studies quasiconformal non-equivalence of Julia sets and limit sets. We proved that any Julia set is quasiconformally different from the Apollonian gasket. We also proved that any Julia set of a quadratic rational map is quasiconformally different from the gasket limit set of a geometrically finite Kleinian group.

Keywords

quasiconformal non-equivalenceJulia setslimit setsApollonian gasketcircle packings

MSC classification

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions
Secondary: 30C62: Quasiconformal mappings in the plane
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , First View , pp. 1 - 25
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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