Global topology of hyperbolic components: Cantor circle case

Global topology of hyperbolic components: Cantor circle case

We prove that in the moduli space Md of degree d⩾2 rational maps, any hyperbolic component in the disconnectedness locus and of Cantor circle type is a finite quotient of R4d−4−n×Tn, where n is determined by dynamics. The proof uses some ideas from Riemann surface theory (Abel's Theorem), dynam...

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Veröffentlicht in:Proceedings of the London Mathematical Society 2017-10, Vol.115 (4), p.897-923, Article 897
Hauptverfasser: Wang, Xiaoguang, Yin, Yongcheng
Format: Artikel
Sprache:eng
Schlagworte:
37F10
37F15 (secondary)
37F45 (primary)
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Zusammenfassung:We prove that in the moduli space Md of degree d⩾2 rational maps, any hyperbolic component in the disconnectedness locus and of Cantor circle type is a finite quotient of R4d−4−n×Tn, where n is determined by dynamics. The proof uses some ideas from Riemann surface theory (Abel's Theorem), dynamical system and algebraic topology.
ISSN:0024-6115
1460-244X
DOI:10.1112/plms.12058