Bounded hyperbolic components of quadratic rational maps

Let \({\cal H}\) be a hyperbolic component of quadratic rational maps possessing two distinct attracting cycles. We show that \({\cal H}\) has compact closure in moduli space if and only if neither attractor is a fixed point.

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Bibliographic Details
Published inarXiv.org
Main Author Epstein, Adam L
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.09.1997
Subjects
Cycle ratio
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Summary:Let \({\cal H}\) be a hyperbolic component of quadratic rational maps possessing two distinct attracting cycles. We show that \({\cal H}\) has compact closure in moduli space if and only if neither attractor is a fixed point.
ISSN:2331-8422