|
This article is cited in 1 scientific paper (total in 1 paper)
Modeling core parts of Zakeri slices I
Alexander Blokha, Leх Oversteegena, Anastasia Shepelevtsevabc, Vladlen Timorinbd a Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170
b Faculty of Mathematics, HSE University, Russian Federation, 6 Usacheva St., 119048 Moscow
c Scuola Normale Superiore, 7 Piazza dei Cavalieri, 56126 Pisa, Italy
d Independent University of Moscow, Bolshoy Vlasyevskiy Per. 11, 119002 Moscow, Russia
Abstract:
The paper deals with cubic 1-variable polynomials whose Julia sets are connected. Fixing a bounded type rotation number, we obtain a slice of such polynomials with the origin being a fixed Siegel point of the specified rotation number. Such slices as parameter spaces were studied by S. Zakeri, so we call them Zakeri slices. We give a model of the central part of a slice (the subset of the slice that can be approximated by hyperbolic polynomials with Jordan curve Julia sets), and a continuous projection from the central part to the model. The projection is defined dynamically and agrees with the dynamical-analytic parameterization of the Principal Hyperbolic Domain by Petersen and Tan Lei.
Key words and phrases:
complex dynamics, Julia set, cubic polynomial, Siegel disk, connectedness locus, external rays.
Citation:
Alexander Blokh, Leх Oversteegen, Anastasia Shepelevtseva, Vladlen Timorin, “Modeling core parts of Zakeri slices I”, Mosc. Math. J., 22:2 (2022), 265–294
Linking options:
https://www.mathnet.ru/eng/mmj828 https://www.mathnet.ru/eng/mmj/v22/i2/p265
|
Statistics & downloads: |
Abstract page: | 16 | References: | 8 |
|