A necessary condition for the absolute continuity of invariant measure of circle maps with countably infinite number of break points
Let f be a circle homeomorphism with countably many break points that is, differentiable except in countably many points where the derivatives have a jump. Assuming its rotation number ρ to be irrational, we provide a necessary condition for the absolute continuity of invariant measure with respect...
| Main Authors: | , , , |
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| Format: | Article |
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Pushpa Publishing House
2017
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| Summary: | Let f be a circle homeomorphism with countably many break points that is, differentiable except in countably many points where the derivatives have a jump. Assuming its rotation number ρ to be irrational, we provide a necessary condition for the absolute continuity of invariant measure with respect to the Lebesgue measure. |
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