Skew products over the irrational rotation
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Here we give conditions on a class of functions defining skew product extensions of irrational rotations on T which ensure ergodicity. These results produce extensions of the work done by P. Hellekalek and G. Larcher [HL1] and [HL2] to the larger class of functions which are piecewise absolutely continuous, have zero integral and have a derivative which is Riemann integrable with a non-zero integral.
KeywordsBorel Function Irrational Number Fixed Proportion Continue Fraction Expansion Irrational Rotation
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