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A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$
Multi angle
Authors : Petersen, Carsten Lunde (Author of the conference)
CIRM (Publisher )
30D05 - Functional equations in the complex domain, iteration and composition of analytic functions
37F31 - Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics
37F46 - Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets
CIRM (Publisher )
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Abstract :
In a recently completed paper Pascale Roesch and I have given a complete proof that the connectedness locus $M_{1}$ in the space moduli space of quadratic rational maps with a parabolic fixed point of multiplier 1 is homeomorphic to the Mandelbrot set. In this talk I will outline and discus the proof, which in an essential way involves puzzles and a theorem on local connectivity of $M_{1}$ at any parameter which is neither renormalizable nor has all fixed points non-repelling similar to Yoccoz celebrated theorem for local connectivity of $M$ at corresponding parameters.
Keywords : Parabolic Mandelbrot set; parabolic Yoccoz puzzles; parabolic Yoccoz parameters; combinatorial analytic invariant
MSC Codes : Keywords : Parabolic Mandelbrot set; parabolic Yoccoz puzzles; parabolic Yoccoz parameters; combinatorial analytic invariant
30D05 - Functional equations in the complex domain, iteration and composition of analytic functions
37F31 - Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics
37F46 - Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/11/2021 Conference Date : 22/09/2021 Subseries : Research talks arXiv category : Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:58:41 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-22_Petersen.mp4 
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Information on the Event
Event Title : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexeEvent Organizers : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk Dates : 20/09/2021 - 24/09/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2546.html
Citation Data
DOI : 10.24350/CIRM.V.19814603Cite this video as: Petersen, Carsten Lunde (2021). A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19814603 URI : http://dx.doi.org/10.24350/CIRM.V.19814603 |
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