Quasisymmetrically inequivalent hyperbolic Julia sets
Peter Haissinsky (LATP), Kevin M. Pilgrim
TL;DR
This paper provides explicit examples of hyperbolic rational map Julia sets that are topologically identical but differ in their quasisymmetric structure, highlighting nuanced geometric distinctions.
Contribution
It introduces explicit examples of hyperbolic Julia sets that are topologically equivalent but not quasisymmetrically homeomorphic, revealing new geometric complexity.
Findings
Julia sets are homeomorphic but not quasisymmetrically equivalent
Explicit examples demonstrate the difference in geometric structures
Highlights limitations of topological equivalence in complex dynamics
Abstract
We give explicit examples of pairs of Julia sets of hyperbolic rational maps which are homeomorphic but not quasisymmetrically homeomorphic.
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