The behavior of renormalizations of circle maps with rational rotation numbers and with Zygmund conditions


  • Habibulla Akhadkulov Universiti Utara Malaysia
  • Abdumajid Begmatov National University of Uzbekistan
  • Teh Yuan Ying Turin Polytechnic University



Renormalization, circle maps, rotation number.


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.

Author Biographies

Abdumajid Begmatov, National University of Uzbekistan

Faculty of Mathematics

Teh Yuan Ying, Turin Polytechnic University

 Department of Natural and Mathematical Sciences


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