A Necessary Condition for the Absolute Continuity of Invariant Measure of Circle Maps With Countably Infinite Number of Break Points

Akhadkulov, Habibulla; Saaban, Azizan; Noorani, Mohd Salmi Md; Akhatkulov, Sokhobiddin

doi:10.17654/ms101030675

Search citation statements

Order By: Relevance

Paper Sections

Select...

Remark1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• Our result complements the main result of [2]. Indeed, in [2], there was obtained a necessary condition for absolute continuity of the invariant measure of P-homeomorphisms with countable infinite number of break points. It is well known that the invariant measure is a conjugacy between a circle homeomorphism and linear rotation.…”

Section: Remarksupporting

confidence: 81%

A Sufficient Condition for the Absolute Continuity of Conjugation Between Circle Homeomorphisms With Breaks

Akhadkulov¹,

Ibrahim²,

Saaban³

et al. 2019

Int. J. of Appl. Math.

View full text Add to dashboard Cite

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 ρ. 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].

show abstract

Section: Remarksupporting

confidence: 81%