A SUFFICIENT CONDITION FOR THE ABSOLUTE
CONTINUITY OF CONJUGATION BETWEEN
CIRCLE HOMEOMORPHISMS WITH BREAKS
Habibulla Akhadkulov1, Haslinda Ibrahim1,
Azizan Saaban2, Sokhobiddin Akhatkulov2
1School of Quantitative Sciences
University Utara Malaysia
CAS 06010, UUM Sintok, Kedah Darul Aman, MALAYSIA
2Faculty of Applied Mathematics and Informatics
Samarkand State University
Boulevard st. 15, 140104 Samarkand, UZBEKISTAN

Abstract

Let $T_{1}$ and $T_{2}$ be circle homeomorphisms with countable many break points, that is, discontinuities in the derivative $T_{1}$ and $T_{2},$ with identical irrational rotation number $\rho.$ Assume that the total variations of $\log DT_{i},$ $i=1,2$ are bounded. We provide a sufficient condition for the absolute continuity of conjugation between $T_{1}$ and $T_{2}.$ The result extends and complements previous obtained results in [2] and [6].

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 2
Year: 2019

DOI: 10.12732/ijam.v32i2.2

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