Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The scenery factor of the ${[T,T^{-1}]}$ transformation is not loosely Bernoulli

Author: Christopher Hoffman
Journal: Proc. Amer. Math. Soc. 131 (2003), 3731-3735
MSC (2000): Primary 28D05
Published electronically: July 9, 2003
MathSciNet review: 1998180
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Kalikow (1982) proved that the $[T,T^{-1}]$transformation is not isomorphic to a Bernoulli shift. We show that the scenery factor of the $[T,T^{-1}]$transformation is not isomorphic to a Bernoulli shift. Moreover, we show that it is not Kakutani equivalent to a Bernoulli shift.

References [Enhancements On Off] (What's this?)

  • 1. I. Benjamini and H. Kesten. Distinguishing sceneries by observing the scenery along a random walk path, J. Anal. Math. 69 (1996), 97-135. MR 98f:60134
  • 2. J. Feldman. New $K$-automorphisms and a problem of Kakutani, Israel J. Math. 24 (1976), no. 1, 16-38. MR 53:13515
  • 3. S. Kalikow. $T,T^{-1}$ transformation is not loosely Bernoulli, Annals of Math. (2) 115 (1982), 393-409. MR 85j:28019
  • 4. J. Kieffer. A direct proof that VWB processes are closed in the $\bar d$-metric, Israel J. Math. 41 (1982), 154-160. MR 84i:28023
  • 5. E. Lindenstrauss. Indistinguishable sceneries, Random Structures Algorithms 14 (1999), No. 1, pp. 71-86. MR 99m:60106
  • 6. H. Matzinger. Reconstructing a 2-color scenery by observing it along a simple random walk path, preprint.
  • 7. I. Meilijson. Mixing properties of a class of skew-products, Israel J. Math. 19 (1974), 266-270. MR 51:8374
  • 8. M. Rahe. Relatively finitely determined implies relatively very weak Bernoulli, Canad. J. Math. 30 (1978), no. 3, 531-548. MR 81j:28029
  • 9. D. Rudolph. If a two-point extension of a Bernoulli shift has an ergodic square, then it is Bernoulli, Israel J. Math. 30 (1978), 159-180. MR 80h:28028a
  • 10. J. Steif. The $T,T^{-1}$-process, finitary codings and weak Bernoulli, Israel Journal of Math. 125 (2001), 29-43. MR 2003a:28025
  • 11. J. Thouvenot. Quelques propriétés des systèmes dynamiques qui se décomposent en un produit de deux systèmes dont l'un est un schéma de Bernoulli, Israel J. Math. 21 (1975), 177-207. MR 53:3263

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 28D05

Retrieve articles in all journals with MSC (2000): 28D05

Additional Information

Christopher Hoffman
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195

Received by editor(s): June 7, 2002
Published electronically: July 9, 2003
Communicated by: Michael Handel
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society