Landing property of stretching rays for real cubic polynomials

Yohei Komori, Shizuo Nakane

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The landing property of the stretching rays in the parameter space of bimodal real cubic polynomials is completely determined. Define the Böttcher vector by the difference of escaping two critical points in the logarithmic Böttcher coordinate. It is a stretching invariant in the real shift locus. We show that stretching rays with non-integral Böttcher vectors have non-trivial accumulation sets on the locus where a parabolic fixed point with multiplier one exists.

Original languageEnglish
JournalConformal Geometry and Dynamics
Volume8
Publication statusPublished - 2004
Externally publishedYes

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Keywords

  • Parabolic implosion
  • Radial Julia set
  • Stretching rays

ASJC Scopus subject areas

  • Mathematics(all)
  • Geometry and Topology

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