2 00 7 Singular measures of circle homeomorphisms with two breakpoints 1
نویسنده
چکیده
Let Tf be a circle homeomorphism with two break points ab, cb and irrational rotation number ̺f . Suppose that the derivative Df of its lift f is absolutely continuous on every connected interval of the set S\{ab, cb}, that DlogDf ∈ L 1 and the product of the jump ratios of Df at the break points is nontrivial, i.e. Df−(ab) Df+(ab) Df − (cb) Df+(cb) 6= 1. We prove that the unique Tf invariant probability measure μf is then singular with respect to Lebesgue measure l on S.
منابع مشابه
Singular Measures in Circle Dynamics
Critical circle homeomorphisms have an invariant measure totally singular with respect to the Lebesgue measure. We prove that singularities of the invariant measure are of Hőlder type. The Hausdorff dimension of the invariant measure is less than 1 but greater than 0.
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