Author:
AKHADKULOV HABIBULLA,DZHALILOV AKHTAM,MAYER DIETER
Abstract
AbstractLetfi∈C2+α(S1∖{ai,bi}),α>0,i=1,2, be circle homeomorphisms with two break pointsai,bi, that is, discontinuities in the derivativeDfi, with identical irrational rotation numberρandμ1([a1,b1])=μ2([a2,b2]), whereμiare the invariant measures offi,i=1,2. Suppose that the products of the jump ratios ofDf1andDf2do not coincide, that is,Df1(a1−0)/Df1(a1+0)⋅Df1(b1−0)/Df1(b1+0)≠Df2(a2−0)/Df2(a2+0)⋅Df2(b2−0)/Df2(b2+0) . Then the mapψconjugatingf1andf2is a singular function, that is, it is continuous onS1, butDψ(x)=0 almost everywhere with respect to Lebesgue measure.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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