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- W4294397256 abstract "Let $f_{i},$ $i=1,2$ be piecewise-smooth $C^{1}$ circle homeomorphisms with two break points, $log Df_{i},$ $i=1,2$ are absolutely continuous on each continuity intervals of $Df_{i}$ and $Dlog Df_{i}in L^{p}$ for some $p>1.$ Suppose, the jump ratios of $f_{1} $ and $f_{2} $ at their break points do not coincide but have the same total jumps (i.e. the product of jump ratios) and identical irrational rotation number of bounded type. Then the conjugation $h$ between $f_{1} $ and $f_{2} $ is a singular function, i.e. it is continuous on $S^1,$ but $Dh(x)=0$ a.e. with respect to Lebesgue measure." @default.
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- W4294397256 date "2013-02-27" @default.
- W4294397256 modified "2023-10-18" @default.
- W4294397256 title "Nonrigidity of piecewise-smooth circle maps" @default.
- W4294397256 doi "https://doi.org/10.48550/arxiv.1302.6691" @default.
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