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
ISSN	1078-0947
DOI	https://doi.org/10.3934/dcds.2017220
Status	Udgivet - 1 okt. 2017

Emneord

holomorphic dynamics

Citer dette

Lomonaco, L., Petersen, C. L., & Shen, W. (2017). On parabolic external maps. Discrete and Continuous Dynamical Systems. Series A, 37(10), 5085-5104. https://doi.org/10.3934/dcds.2017220

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AU - Shen, Weixiao

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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.

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