Entire functions with Cantor bouquet Julia sets

Autor: Pardo-Simón, Leticia, Rempe, Lasse

A hyperbolic transcendental entire function with connected Fatou set is said to be of disjoint type. It is known that the Julia set of a disjoint-type function of finite order is a Cantor bouquet; in particular, it is a collection of arcs (''hairs'')

Externí odkaz: http://arxiv.org/abs/2209.03284

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Cantor bouquet of holomorphic stable manifolds for a periodic indeterminate point

Autor: Yoshikazu Yamagishi

Publikováno v: Nonlinearity. 14:113-120

In the rational dynamics of the complex projective plane, we construct a full 2-shift family of holomorphic stable manifolds of a periodic indeterminate point with two periodic orbits.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::1aa109e013a79eab6eb2b2db14e8fcd7
https://doi.org/10.1088/0951-7715/14/1/306

Another construction of a Cantor bouquet at a fixed indeterminate point

Autor: Tomoko Shinohara

Publikováno v: Kyoto J. Math. 50, no. 1 (2010), 205-224

In this article, we study the local dynamical structure of a rational mapping $F$ of $\mathbf{P}^{2}$ at a fixed indeterminate point $p$ . Using a sequence of blowups, we construct a family $\{\tilde{W}_{\mathbf{j}}\}_{{\mathbf{j}}\in J}$ of germs of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::949e6ac18d99908a20236e136639ab55
http://projecteuclid.org/euclid.kjm/1271187744

Brushing the hairs of transcendental entire functions

Autor: Krzysztof Barański, Lasse Rempe, Xavier Jarque

Publikováno v: Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Recercat. Dipósit de la Recerca de Catalunya
instname

Let f be a hyperbolic transcendental entire function of finite order in the Eremenko-Lyubich class (or a finite composition of such maps), and suppose that f has a unique Fatou component. We show that the Julia set of $f$ is a Cantor bouquet; i.e. is

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e8650d52f6046cda70d73605938f21b
http://hdl.handle.net/2072/410472