The behavior of renormalizations of circle maps with rational rotation numbers and with Zygmund conditions
DOI:
https://doi.org/10.11113/mjfas.v16n4.1725Keywords:
Renormalization, circle maps, rotation number.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.
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