A SUFFICIENT CONDITION FOR THE ABSOLUTE CONTINUITY OF CONJUGATION BETWEEN CIRCLE HOMEOMORPHISMS WITH BREAKS
Habibulla AkhadkulovSchool of Quantitative Sciences University Utara Malaysia CAS 06010, UUM Sintok, Kedah Darul Aman, MALAYSIAHariwan Z. IbrahimSchool of Quantitative Sciences University Utara Malaysia CAS 06010, UUM Sintok, Kedah Darul Aman, MALAYSIAAzizan SaabanSchool of Quantitative Sciences University Utara Malaysia CAS 06010, UUM Sintok, Kedah Darul Aman, MALAYSIASokhobiddin AkhatkulovFaculty of Applied Mathematics and Informatics Samarkand State University Boulevard st. 15, 140104 Samarkand, UZBEKISTAN
ABI
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 . 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].
Topics
Identifiers
Citations and references
Cited by 09 references
Metrics — AkademScholar · Coming soon