Most monothetic extensions are rank-1

Analytic cocycles of type $I I I_{0}$ over an irrational rotation are constructed and an example of that type is given, where all corresponding special flows are weakly mixing.

Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios

Ryotaro Sato (2006)

Commentationes Mathematicae Universitatis Carolinae

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Using the ratio ergodic theorem for a measure preserving transformation in a $σ$ -finite measure space we give a straightforward proof of Derriennic’s reverse maximal inequality for the supremum of ergodic ratios.

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