| Popis: |
Let f i , i = 1 , 2 , be piecewise C 1 circle homeomorphisms with two break points, log D f i , i = 1 , 2 , are absolutely continuous on each continuity interval of D f i and D log D f i ∈ L p for some p > 1 . Suppose, the jump ratios of f 1 and f 2 at their break points do not coincide but f 1 , f 2 have the same total jumps (i.e. the product of jump ratios) and identical irrational rotation number of bounded type. Then the map h conjugating f 1 and f 2 is a singular function, that is, it is continuous on S 1 , but D h ( x ) = 0 almost everywhere with respect to Lebesgue measure. |
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