A necessary condition for the absolute continuity of invariant measure of circle maps with countably infinite number of break points

• Main Authors: Akhadkulov, Habibulla, Saaban, Azizan, Md Noorani, Mohd Salmi, Akhatkulov, Sokhobiddin
• Format: Article
• Published: Pushpa Publishing House 2017
• Subjects: Q Science (General)
• Online Access: http://repo.uum.edu.my/21961/; http://doi.org/10.17654/MS101030675

Let f be a circle homeomorphism with countably many break points that is, differentiable except in countably many points where the derivatives have a jump. Assuming its rotation number ρ to be irrational, we provide a necessary condition for the absolute continuity of invariant measure with respect...