Work

Hyperbolic components of McMullen maps

Year: 2012

Type: preprint

Abstract: In this article, we study the hyperbolic components of McMullen maps. We show that the boundaries of all hyperbolic components are Jordan curves. This settles a problem posed by Devaney. As a consequence, we show that cusps are dense on the boundary of the unbounded hyperbolic component. This is a dynamical analogue of McMullen's theorem that cusps are dense on the Bers' boundary of Teichmüller space.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1207.0266

Authors: Qiu, Weiyuan, Roesch, Pascale, Wang, Xiaoguang, Yin, Yongcheng

Institutions: Fudan University, Institut de Mathématiques de Marseille, Zhejiang University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2155334331

Cites: 19

Cited by: 3

Related to: 10