Hausdorffization and polynomial twists

Laura DeMarco; Kevin Pilgrim

doi:10.3934/dcds.2011.29.1405

Hausdorffization and polynomial twists

Laura DeMarco^*, Kevin Pilgrim

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study dynamical equivalence relations on the moduli space MPd of complex polynomial dynamical systems. Our main result is that the critical-heights quotient MP_d → T ^* _d of [4] is the Hausdorzation of a relation based on the twisting deformation of the basin of infinity. We also study relations of topological conjugacy and the Branner-Hubbard wringing deformation.

Original language	English (US)
Pages (from-to)	1405-1417
Number of pages	13
Journal	Discrete and Continuous Dynamical Systems
Volume	29
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2011.29.1405
State	Published - Apr 2011

Keywords

Conjugacy classes
Equivalence relations
Hausdorffization
Polynomial dynamics
Quasiconformal deformation

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2011.29.1405

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abstract = "We study dynamical equivalence relations on the moduli space MPd of complex polynomial dynamical systems. Our main result is that the critical-heights quotient MPd → T * d of [4] is the Hausdorzation of a relation based on the twisting deformation of the basin of infinity. We also study relations of topological conjugacy and the Branner-Hubbard wringing deformation.",

keywords = "Conjugacy classes, Equivalence relations, Hausdorffization, Polynomial dynamics, Quasiconformal deformation",

author = "Laura DeMarco and Kevin Pilgrim",

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AB - We study dynamical equivalence relations on the moduli space MPd of complex polynomial dynamical systems. Our main result is that the critical-heights quotient MPd → T * d of [4] is the Hausdorzation of a relation based on the twisting deformation of the basin of infinity. We also study relations of topological conjugacy and the Branner-Hubbard wringing deformation.

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KW - Polynomial dynamics

KW - Quasiconformal deformation

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Hausdorffization and polynomial twists

Abstract

Keywords

ASJC Scopus subject areas

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