On Critical Circle Homeomorphisms with Infinite Number of Break Points - Akhtam Dzhalilov; Mohd Salmi Md Noorani; Sokhobiddin Akhatkulov (Abstract and Applied Analysis)
We prove that a critical circle homeomorphism with infinite number of break points without periodic orbits is conjugated to the linear rotation by a quasisymmetric map if and only if its rotation number is of bounded type. And we also prove that any two adjacent atoms of dynamical partition of a unit circle are comparable.