Pure strictly uniform models of non-ergodic measure automorphisms

Strictly ergodic, uniform positive entropy models

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Uniform Szego cocycles over strictly ergodic subshifts

We consider ergodic families of Verblunsky coefficients generated by minimal aperiodic subshifts. Simon conjectured that the associated probability measures on the unit circle have essential support of zero Lebesgue measure. We prove this for a large class of subshifts, namely those satisfying Boshernitzan’s condition. This is accomplished by relating the essential support to uniform convergenc...

On Strictly Ergodic Models Which Are Not Almost Topologically Conjugate

Answering a question raised by Glasner and Rudolph (1984) we construct uncountably many strictly ergodic topological systems which are metrically isomorphic to a given ergodic system (X,63, #, T) but not almost topologically conjugate to it.

Existence of Non-uniform Cocycles on Uniquely Ergodic Systems

Ergodic properties of quantized toral automorphisms

We study the ergodic properties for a class of quantized toral automorphisms, namely the cat and Kronecker maps. The present work uses and extends the results of [KL]. We show that quantized cat maps are strongly mixing, while Kronecker maps are ergodic and nonmixing. We also study the structure of these quantum maps and show that they are effected by unitary endomorphisms of a suitable vector ...