On (non-)local-connectivity of some Julia sets
File(s)
Accepted version
Author(s)
Dezotti, A
Roesch, P
Type
Journal Article
Abstract
We show that Arnold tongues for the family of double standard maps
f_{a,b}(x)=2x+a-(b/\pi)sin(2 \pi x)
are connected. This proof is accomplished in the complex domain by means of quasiconformal techniques and depends partly upon the fact that the complexification of f_{a,b}, has only one critical orbit taking symmetry into account.
f_{a,b}(x)=2x+a-(b/\pi)sin(2 \pi x)
are connected. This proof is accomplished in the complex domain by means of quasiconformal techniques and depends partly upon the fact that the complexification of f_{a,b}, has only one critical orbit taking symmetry into account.
Date Issued
2010-04-07
Date Acceptance
2009-04-01
Citation
Proceedings of the American Mathematical Society, 2010, 138, pp.3569-3583
ISSN
1088-6826
Publisher
American Mathematical Society
Start Page
3569
End Page
3583
Journal / Book Title
Proceedings of the American Mathematical Society
Volume
138
Copyright Statement
© Copyright 2010 American Mathematical Society
Identifier
http://arxiv.org/abs/1203.2741v1
Subjects
math.DS
math.CV
Notes
28 pages, 3 figures