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Criniferous entire maps with absorbing Cantor bouquets
- Publication Year :
- 2020
-
Abstract
- It is known that, for many transcendental entire functions in the Eremenko-Lyubich class $\mathcal{B}$, every escaping point can eventually be connected to infinity by a curve of escaping points. When this is the case, we say that the functions are criniferous. In this paper, we extend this result to a new class of maps in $\mathcal{B}$. Furthermore, we show that if a map belongs to this class, then its Julia set contains a Cantor bouquet; in other words, it is a subset of $\mathbb{C}$ ambiently homeomorphic to a straight brush.<br />V2: Author accepted manuscript. To appear in Discrete Contin. Dyn. Syst
- Subjects :
- Class (set theory)
Mathematics::Dynamical Systems
Mathematics - Complex Variables
Applied Mathematics
media_common.quotation_subject
Entire function
Mathematics::General Topology
Dynamical Systems (math.DS)
Infinity
Julia set
Combinatorics
FOS: Mathematics
Discrete Mathematics and Combinatorics
Point (geometry)
Transcendental number
Complex Variables (math.CV)
Mathematics - Dynamical Systems
Analysis
media_common
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....f68055a765786ebd5022f75a21d889ef