Quasi-symmetric Conjugacy of Blaschke Products on the unit Circle

Carsten Lunde Petersen

doi:10.1112/blms/bdm055

Quasi-symmetric Conjugacy of Blaschke Products on the unit Circle

Carsten Lunde Petersen

Mathematics and Physics (IMFUFA)

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

Let B be a Blaschke product for which the restriction to theunit circle $S$ ¹ is a degree d > 1 covering. We prove that Bis quasi-symmetrically conjugate to z ${rightarrowtail}$ z^d on $S$ ¹, if all its periodicpoints in $S$ ¹ are repelling and if $S$ ¹ does not intersect the ${omega}$ -limitset of any recurrent critical point for B.

Translated title of the contribution	Quasi-Symmetrisk konjugation af Blaschke produkter på enhedscirklen
Original language	English
Journal	Bulletin of the London Mathematical Society
Volume	39
Issue number	5
Pages (from-to)	724-730
Number of pages	7
ISSN	0024-6093
DOIs	https://doi.org/10.1112/blms/bdm055
Publication status	Published - 2007

Keywords

quasi-symmetric conjugacy
Blaschke product
recurrent critical points

Link to document

10.1112/blms/bdm055

http://blms.oxfordjournals.org/cgi/reprint/bdm055?

Cite this

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title = "Quasi-symmetric Conjugacy of Blaschke Products on the unit Circle",

abstract = "Let B be a Blaschke product for which the restriction to the unit circle 1 is a degree d > 1 covering. We prove that B is quasi-symmetrically conjugate to z zd on 1, if all its periodic points in 1 are repelling and if 1 does not intersect the -limit set of any recurrent critical point for B. ",

keywords = "quasi-symmetrisk konjugation, Blaschke Product, rekurrente kritiske punkter, quasi-symmetric conjugacy, Blaschke product, recurrent critical points",

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AB - Let B be a Blaschke product for which the restriction to the unit circle 1 is a degree d > 1 covering. We prove that B is quasi-symmetrically conjugate to z zd on 1, if all its periodic points in 1 are repelling and if 1 does not intersect the -limit set of any recurrent critical point for B.

KW - quasi-symmetrisk konjugation

KW - Blaschke Product

KW - rekurrente kritiske punkter

KW - quasi-symmetric conjugacy

KW - Blaschke product

KW - recurrent critical points

U2 - 10.1112/blms/bdm055

DO - 10.1112/blms/bdm055

M3 - Journal article

SN - 0024-6093

VL - 39

SP - 724

EP - 730

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 5

ER -