References & Citations
Mathematics > Dynamical Systems
Title: The Parabolic Mandelbrot Set
(Submitted on 20 Jul 2021 (v1), last revised 11 Apr 2024 (this version, v2))
Abstract: We solve the longstanding conjecture by Milnor (1993) concerning the connectedness locus $M_1$ of the family of quadratic rational maps tangent to the identity at $\infty$. We prove that this locus in homeomorphic to the Mandelbrot set $M$ and that the homeomorphism is unique, provided it identifies maps that are "hybridly" conjugate on their filled-in Julia set. Moreover this homeomorphism from $M$ to $M_1$ is nowhere H\"older on the boundary and so can not have even locally a quasi-conformal extension to complements.
Submission history
From: Carsten Petersen L [view email][v1] Tue, 20 Jul 2021 11:10:03 GMT (4448kb,D)
[v2] Thu, 11 Apr 2024 13:29:53 GMT (12331kb,D)
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