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Remarks on the period three cycles of quadratic rational maps

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Abstract

Milnor showed that the moduli space of Mobius conjugacy classes of quadratic rational maps of the complex projective line to itself is canonically biholomorphic to C-2. Moreover, the affine structure on C-2 has dynamical relevance: the loci Per(n) (eta) consisting of maps with an n-cycle of multiplier eta are affine lines for n = 1 and n = 2. The loci Per(3) (eta) are cubic algebraic curves. In this work, we further the investigation of the family of cubics Per(3)(eta)

Topics: QA, QC
Publisher: IOP PUBLISHING LTD
OAI identifier: oai:wrap.warwick.ac.uk:10097
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