En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK

Documents 54F15 2 résultats

Filtrer
Sélectionner : Tous / Aucun
Q
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
y

Wandering lakes of Wada - Martí-Pete, David (Auteur de la conférence) | CIRM H

Multi angle

We construct a transcendental entire function for which infinitely many Fatou components share the same boundary. This solves the long-standing open problem whether Lakes of Wada continua can arise in complex dynamics, and answers the analogue of a question of Fatou from 1920 concerning Fatou components of rational functions. Our theorem also provides the first example of an entire function having a simply connected Fatou component whose closure has a disconnected complement, answering a recent question of Boc Thaler. Using the same techniques, we give new counterexamples to a conjecture of Eremenko concerning curves in the escaping set of an entire function. This is joint work with Lasse Rempe and James Waterman.[-]
We construct a transcendental entire function for which infinitely many Fatou components share the same boundary. This solves the long-standing open problem whether Lakes of Wada continua can arise in complex dynamics, and answers the analogue of a question of Fatou from 1920 concerning Fatou components of rational functions. Our theorem also provides the first example of an entire function having a simply connected Fatou component whose closure ...[+]

37F10 ; 30D05 ; 37B45 ; 54F15

Sélection Signaler une erreur
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
y

Entire functions with Cantor bouquet Julia sets - Pardo-Simon, Leticia (Auteur de la conférence) | CIRM H

Virtualconference

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.[-]
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 ...[+]

37F10 ; 54H20 ; 30D05 ; 54F15

Sélection Signaler une erreur