Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters

DOI10.1090/jams/942zbMath1457.37061arXiv1703.01206OpenAlexW3036117205MaRDI QIDQ3300663

Nikita Selinger, Mikhail Lyubich, Dzmitry Dudko

Publication date: 29 July 2020

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.01206

zbMATH Keywords

periodic pointshyperbolicityMandelbrot setSiegel parametersSiegel renormalization

Mathematics Subject Classification ID

Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Renormalization of holomorphic dynamical systems (37F25) Rotation numbers and vectors (37E45) Combinatorics and topology in relation with holomorphic dynamical systems (37F20) Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets (37F46) Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps (37F44)

Related Items (6)

Parabolic bifurcation loci in the spaces of rational functions ⋮ On critical renormalization of complex polynomials ⋮ Dynamics of Schwarz Reflections: The Mating Phenomena ⋮ Local connectivity of the Mandelbrot set at some satellite parameters of bounded type ⋮ Renormalization in the golden-mean semi-Siegel Hénon family: universality and non-rigidity ⋮ Lebesgue measure of Feigenbaum Julia sets

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