No abstract

No abstract

Let  be one-parameter family of circle homeomorphisms with a break point, that is, the derivative  has jump discontinuity at this point. Suppose  satisfies a certain Zygmund condition which is dependent on parameter . We prove that the renormalizations of circle homeomorphisms from this family with rational rotation number of sufficiently large rank are approximated by piecewise fractional linear transformations in  and -norms, depending on the values of the parameter   and , respectively.

No abstract

A class of topological equivalent generalized interval exchange maps of genus one and of the same bounded combinatorics is considered in the paper. A sufficient condition for absolute continuity of the conjugation between two maps from this class is provided