Potential Analysis

, Volume 44, Issue 1, pp 43–51 | Cite as

Furstenberg Transformations on Cartesian Products of Infinite-Dimensional Tori



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.


Furstenberg transformations Infinite-dimensional torus Commutator methods 

Mathematics Subject Classifications (2010)

28D10 37A30 37C40 58J51 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Departamento de Matemática y Ciencia de la ComputaciónUniversidad de Santiago de ChileEstación CentralChile
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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