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arXiv · 1501.06245

Furstenberg transformations on Cartesian products of infinite-dimensional tori

P. A. Cecchi·R. Tiedra de Aldecoa
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Abstract

We consider in this note Furstenberg transformations on Cartesian products of infinite-dimensional tori. Under some appropriate assumptions, we show that these transformations are uniquely ergodic with respect to the Haar measure and have countable Lebesgue spectrum in a suitable subspace. These results generalise to the infinite-dimensional setting previous results of H. Furstenberg, A. Iwanik, M. Lemanzyk, D. Rudolph and the second author in the one-dimensional setting. Our proofs rely on the use of commutator methods for unitary operators and Bruhat functions on the infinite-dimensional torus.

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P. A. Cecchi, R. Tiedra de Aldecoa. 2015-01-26. Furstenberg transformations on Cartesian products of infinite-dimensional tori. https://arxiv.org/abs/1501.06245

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