Landing property of stretching rays for real cubic polynomials

Komori, Yohei; Nakane, Shizuo

doi:10.1090/S1088-4173-04-00102-X

Landing property of stretching rays for real cubic polynomials
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by Yohei Komori and Shizuo Nakane

Conform. Geom. Dyn. 8 (2004), 87-114

DOI: https://doi.org/10.1090/S1088-4173-04-00102-X

Published electronically: March 29, 2004

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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.

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