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Entire functions with Cantor bouquet Julia sets
Virtualconference
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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}
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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}
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Information on the Video
Language : EnglishAvailable 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 
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Information on the Event
Event Title : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexeDates : 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: (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 |
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