Français
Entire functions with Cantor bouquet Julia sets
Virtualconference
Authors : Pardo-Simon, Leticia (Author of the conference)
CIRM (Publisher )
30D05 - Functional equations in the complex domain, iteration and composition of analytic functions
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
54F15 - Continua and generalizations
54H20 - Topological dynamics, See also {28Dxx, 34C35, 58Fxx}
CIRM (Publisher )
Loading the player...
|
Abstract :
A transcendental entire function with bounded singular set that is hyperbolic and has a unique Fatou component is said to be of disjoint type. The Julia set of any disjoint-type function of finite order is known to be a collection of curves that escape to infinity and form a Cantor bouquet, i.e., a subset of $\mathbb{C}$ ambiently homeomorphic to a straight brush. We show that there exists $f$ of disjoint type whose Julia set $J(f)$ is a collection of escaping curves, but $J(f)$ is not a Cantor bouquet. On the other hand, we prove that if $f$ of disjoint type and $J(f)$ contains an absorbing Cantor bouquet, that is, a Cantor bouquet to which all escaping points are eventually mapped, then $J(f)$ must be a Cantor bouquet. This is joint work with L. Rempe.
Keywords : Cantor bouquet; transcendental entire maps; Julia set
MSC Codes : Keywords : Cantor bouquet; transcendental entire maps; Julia set
30D05 - Functional equations in the complex domain, iteration and composition of analytic functions
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
54F15 - Continua and generalizations
54H20 - Topological dynamics, See also {28Dxx, 34C35, 58Fxx}
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/11/2021 Conference Date : 20/09/2021 Subseries : Research talks arXiv category : Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE ; Topology Format : MP4 (.mp4) - HD Video Time : 00:27:20 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-20_Pardo-Simon.mp4 
|
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.19814303Cite this video as: Pardo-Simon, Leticia (2021). Entire functions with Cantor bouquet Julia sets. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19814303 URI : http://dx.doi.org/10.24350/CIRM.V.19814303 |
See Also
- [Virtualconference] Renormalization in complex dynamics / Author of the conference Shishikura, Mitsuhiro.
- [Multi angle] Characterizing Thurston maps by lifting trees / Author of the conference Winarski, Rebecca.
- [Multi angle] Docile transcendental entire functions / Author of the conference Waterman, James.
- [Virtualconference] Characterizing rational maps positively using graphs / Author of the conference Thurston, Dylan.
- [Multi angle] Transcendental Thurston Theory for entire functions and compositions / Author of the conference Shemyakov, Sergey.
- [Multi angle] Iterated monodromy groups and transcendental dynamics / Author of the conference Reinke, Bernhard.
- [Multi angle] A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$ / Author of the conference Petersen, Carsten Lunde.
- [Multi angle] Contracting self-similar groups and conformal dimension / Author of the conference Nekrashevych, Volodymyr.
- [Virtualconference] Interbreeding in conformal dynamics, and its applications near and far / Author of the conference Mukherjee, Sabyasachi.
- [Multi angle] Wandering lakes of Wada / Author of the conference Martí-Pete, David.
- [Multi angle] Story of the Feigenbaum point / Author of the conference Lyubich, Mikhail.
- [Multi angle] Transcendental Julia sets of minimal Hausdorff dimension / Author of the conference Lazebnik, Kirill.
- [Multi angle] Introduction to Thurston's theorems / Author of the conference Hubbard, John H..
- [Multi angle] Decomposition results in rational dynamics / Author of the conference Hlushchanka, Mikhail.
- [Multi angle] Meromorphic maps of finite type: parameter space / Author of the conference Fagella, Nuria.
- [Multi angle] Hyperbolicity of renormalization for bi-cubic circle maps with bounded combinatorics / Author of the conference Estevez Jacinto, Gabriela Alexandra.
- [Virtualconference] Near-degenerate regime in neutral renormalization / Author of the conference Dudko, Dzmitry.
- [Multi angle] Box renormalization as a 'black box' / Author of the conference Drach, Kostiantyn.
- [Virtualconference] Arithmetic geometric models for the renormalisation of irrationally indifferent attractors / Author of the conference Cheraghi, Davoud.
- [Virtualconference] Tips of tongues in the double standard family / Author of the conference Buff, Xavier.
- [Multi angle] Eremenko's conjecture, Devaney's hairs, and the growth of counterexamples / Author of the conference Brown, Andrew.
- [Virtualconference] The visual sphere of an expanding Thurston map / Author of the conference Bonk, Mario.
- [Multi angle] Transcendental dynamics and infinite-dimensional Thurston theory / Author of the conference Bogdanov, Konstantin.
- [Virtualconference] Transcendental functions with small singular sets / Author of the conference Bishop, Christopher.
- [Multi angle] Polynomial versus transcendental dynamics / Author of the conference Benini, Anna Miriam.
- [Multi angle] Quadratic polynomials / Author of the conference Bartholdi, Laurent.
Bibliography
