Furstenberg transformations on Cartesian products of infinite-dimensional tori

Autor:	Cecchi, P. A., de Aldecoa, R. Tiedra
Rok vydání:	2015
Předmět:	Mathematics - Dynamical Systems Mathematics - Spectral Theory 28D10 37A30 37C40 58J51
Druh dokumentu:	Working Paper
Popis:	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. Comment: 8 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1501.06245 Zobrazit plný text záznamu View this record from Arxiv