INVARIANT MEASURE OF CRITICAL CIRCLE HOMEOMORPHISMS WITH COUNTABLE NUMBER OF BREAKS
Keywords:
circle homeomorphism, rotation number, invariant measure, critical point, break point.Abstract
It is proved that invariant measures of P -homeomorphisms of a circle with countable
many break points and with single critical point, and an irrational rotation number are
singular with respect to the Lebesgue measure on the circle.
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