On parabolic external maps

Luna Lomonaco; Carsten Lunde Petersen; Weixiao Shen

doi:10.3934/dcds.2017220

On parabolic external maps

Luna Lomonaco, Carsten Lunde Petersen, Weixiao Shen

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

Abstract

We prove that any C1+BV degree d ≥ 2 circle covering h having all periodic orbits weakly expanding, is conjugate by a C1+BV diffeomorphism to a metrically expanding map. We use this to connect the space of parabolic external maps (coming from the theory of parabolic-like maps) to metrically expanding circle coverings.

Originalsprog	Engelsk
Tidsskrift	Discrete and Continuous Dynamical Systems. Series A
Vol/bind	37
Udgave nummer	10
Sider (fra-til)	5085-5104
Antal sider	20
ISSN	1078-0947
DOI	https://doi.org/10.3934/dcds.2017220
Status	Udgivet - 1 okt. 2017

Emneord

holomorphic dynamics

Link til dokument

10.3934/dcds.2017220

https://arxiv.org/pdf/1603.01609.pdf

Holomorpic Dynamics and Orthogonal Polynomials
Petersen, C. L. (Anden), Petersen, H. L. (Projektdeltager), Henriksen, C. (Projektdeltager) & Christiansen, J. S. (Projektdeltager)
01/11/2015 → 31/10/2018
Projekter: Projekt › Forskning

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title = "On parabolic external maps",

abstract = "We prove that any C1+BV degree d ≥ 2 circle covering h having all periodic orbits weakly expanding, is conjugate by a C1+BV diffeomorphism to a metrically expanding map. We use this to connect the space of parabolic external maps (coming from the theory of parabolic-like maps) to metrically expanding circle coverings.",

keywords = "holomorphic dynamics, Circle covering, Metric expanding, Parabolic external map, Parabolic-like map, Smooth conjugacy",

author = "Luna Lomonaco and Petersen, {Carsten Lunde} and Weixiao Shen",

year = "2017",

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doi = "10.3934/dcds.2017220",

language = "English",

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TY - JOUR

T1 - On parabolic external maps

AU - Lomonaco, Luna

AU - Petersen, Carsten Lunde

AU - Shen, Weixiao

PY - 2017/10/1

Y1 - 2017/10/1

N2 - We prove that any C1+BV degree d ≥ 2 circle covering h having all periodic orbits weakly expanding, is conjugate by a C1+BV diffeomorphism to a metrically expanding map. We use this to connect the space of parabolic external maps (coming from the theory of parabolic-like maps) to metrically expanding circle coverings.

AB - We prove that any C1+BV degree d ≥ 2 circle covering h having all periodic orbits weakly expanding, is conjugate by a C1+BV diffeomorphism to a metrically expanding map. We use this to connect the space of parabolic external maps (coming from the theory of parabolic-like maps) to metrically expanding circle coverings.

KW - holomorphic dynamics

KW - Circle covering

KW - Metric expanding

KW - Parabolic external map

KW - Parabolic-like map

KW - Smooth conjugacy

U2 - 10.3934/dcds.2017220

DO - 10.3934/dcds.2017220

M3 - Journal article

SN - 1078-0947

VL - 37

SP - 5085

EP - 5104

JO - Discrete and Continuous Dynamical Systems. Series A

JF - Discrete and Continuous Dynamical Systems. Series A

IS - 10

ER -

On parabolic external maps

Abstract

Emneord

Link til dokument

Projekter

Holomorpic Dynamics and Orthogonal Polynomials

Citer dette