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Dynamics of McMullen maps
- Source :
- Advances in Mathematics. 229(4):2525-2577
- Publication Year :
- 2012
- Publisher :
- Elsevier BV, 2012.
-
Abstract
- In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to a question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that the boundary is a quasi-circle if it contains neither a parabolic point nor a recurrent critical point. For the whole Julia set, we show that the McMullen maps have locally connected Julia sets except in some special cases.<br />Complex dynamics, 51 pages, 13 figures
- Subjects :
- Pure mathematics
Mathematics(all)
Yoccoz puzzle
Mathematics::Dynamical Systems
General Mathematics
Mathematical analysis
Local connectivity
Dynamical Systems (math.DS)
McMullen map
37F45
Julia set
Jordan curve theorem
Critical point (mathematics)
symbols.namesake
FOS: Mathematics
symbols
Mathematics - Dynamical Systems
Mathematics
Subjects
Details
- ISSN :
- 00018708
- Volume :
- 229
- Issue :
- 4
- Database :
- OpenAIRE
- Journal :
- Advances in Mathematics
- Accession number :
- edsair.doi.dedup.....274c47f319be3c8caa4eb3945fb1535f
- Full Text :
- https://doi.org/10.1016/j.aim.2011.12.026