### 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 language | English |
---|---|

Journal | Conformal Geometry and Dynamics |

Volume | 8 |

Publication status | Published - 2004 |

Externally published | Yes |

### Fingerprint

### Keywords

- Parabolic implosion
- Radial Julia set
- Stretching rays

### ASJC Scopus subject areas

- Mathematics(all)
- Geometry and Topology

### Cite this

*Conformal Geometry and Dynamics*,

*8*.

**Landing property of stretching rays for real cubic polynomials.** / Komori, Yohei; Nakane, Shizuo.

Research output: Contribution to journal › Article

*Conformal Geometry and Dynamics*, vol. 8.

}

TY - JOUR

T1 - Landing property of stretching rays for real cubic polynomials

AU - Komori, Yohei

AU - Nakane, Shizuo

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - Parabolic implosion

KW - Radial Julia set

KW - Stretching rays

UR - http://www.scopus.com/inward/record.url?scp=18444409630&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18444409630&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18444409630

VL - 8

JO - Conformal Geometry and Dynamics

JF - Conformal Geometry and Dynamics

SN - 1088-4173

ER -