Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

Collection Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

Organizer(s) Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk

Date(s) 20/09/2021 - 24/09/2021

linked URL https://conferences.cirm-math.fr/2546.html

00:00:00 / 00:00:00

18 27

A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$

By Carsten Lunde Petersen

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.

Information about the video

Date of recording 22/09/2021
Date of publication 02/11/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19814603
Cite this video Petersen, Carsten Lunde (22/09/2021). A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19814603
URL https://dx.doi.org/10.24350/CIRM.V.19814603

Domain(s)

Dynamical Systems

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

All the collection videos

26:01

published on November 2, 2021

Wandering lakes of Wada

By David Martí-Pete

59:08

published on November 2, 2021

Contracting self-similar groups and conformal dimension

By Volodymyr Nekrashevych

29:23

published on November 2, 2021

Docile transcendental entire functions

By James Waterman

01:01:26

published on November 2, 2021

Quadratic polynomials

By Laurent Bartholdi

01:02:49

published on November 2, 2021

Interbreeding in conformal dynamics, and its applications near and far

By Sabyasachi Mukherjee

01:06:44

published on November 2, 2021

Renormalization in complex dynamics

By Mitsuhiro Shishikura

59:24

published on November 2, 2021

Characterizing Thurston maps by lifting trees

By Rebecca Winarski

01:05:21

published on November 2, 2021

Transcendental functions with small singular sets

By Christopher Bishop

21:59

published on November 2, 2021

Eremenko's conjecture, Devaney's hairs, and the growth of counterexamples

By Andrew Brown

59:25

published on November 2, 2021

Introduction to Thurston's theorems

By John H. Hubbard

27:20

published on November 2, 2021

Entire functions with Cantor bouquet Julia sets

By Leticia Pardo-Simon

32:47

published on November 2, 2021

Hyperbolicity of renormalization for bi-cubic circle maps with bounded combinatorics

By Gabriela Alexandra Estevez Jacinto

35:40

published on November 2, 2021

Transcendental Julia sets of minimal Hausdorff dimension

By Kirill Lazebnik

28:13

published on November 2, 2021

Iterated monodromy groups and transcendental dynamics

By Bernhard Reinke

01:11:08

published on November 2, 2021

Characterizing rational maps positively using graphs

By Dylan Thurston

01:03:26

published on November 2, 2021

Near-degenerate regime in neutral renormalization

By Dzmitry Dudko

59:41

published on November 2, 2021

Meromorphic maps of finite type: parameter space

By Nuria Fagella

$A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$$
58:41

published on November 2, 2021

A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$

By Carsten Lunde Petersen

33:58

published on November 2, 2021

Transcendental dynamics and infinite-dimensional Thurston theory

By Konstantin Bogdanov

01:06:58

published on November 2, 2021

The visual sphere of an expanding Thurston map

By Mario Bonk

01:02:26

published on November 2, 2021

Arithmetic geometric models for the renormalisation of irrationally indifferent attractors

By Davoud Cheraghi

01:04:27

published on November 2, 2021

Box renormalization as a 'black box'

By Kostiantyn Drach

01:13:51

published on November 2, 2021

Story of the Feigenbaum point

By Mikhail Lyubich

32:19

published on November 2, 2021

Transcendental Thurston Theory for entire functions and compositions

By Sergey Shemyakov

01:05:00

published on November 2, 2021

Tips of tongues in the double standard family

By Xavier Buff

54:58

published on November 2, 2021

Decomposition results in rational dynamics

By Mikhail Hlushchanka

54:47

published on November 2, 2021

Polynomial versus transcendental dynamics

By Anna Miriam Benini

Copyright Carmin.tv 2024

Give feedback