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)



Smorodinsky's conjecture on rank-one mixing

Author: Terrence M. Adams
Journal: Proc. Amer. Math. Soc. 126 (1998), 739-744
MSC (1991): Primary 28D05
MathSciNet review: 1443143
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove Smorodinsky's conjecture: the rank-one transformation, obtained by adding staircases whose heights increase consecutively by one, is mixing.

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

  • [AF] T.M. Adams and N.A. Friedman, Staircase mixing, Ergod. Th. & Dynam. Sys., to appear.
  • [BH] J.R. Blum and D.L. Hanson, On the mean ergodic theorem for subsequences, Bull. Amer. Math. Soc. 55 (1960), 308-311. MR 22:9572
  • [CN] J.R. Choksi and M.G. Nadkarni, The maximal spectral type of a rank-one transformation, Canad. Math. Bull. 37(1) (1994), 29-36. MR 95g:28027
  • [F1] N.A. Friedman, Introduction to Ergodic Theory, Van Nostrand Reinhold, New York, (1970). MR 55:8310
  • [F2] N.A. Friedman, Mixing on sequences, Can. J. Math. 35 (1983), 339-352. MR 85a:28011
  • [Ka] S. Kalikow, Twofold mixing implies threefold mixing for rank-one transformations, Ergod. Th. & Dynam. Sys. 4 (1984), 237-259. MR 86i:28023
  • [Ki] J.L. King, Joining-rank and the structure of finite rank mixing transformations, J. Analyse Math. 51 (1988), 182-227. MR 89k:28009
  • [Kl] I. Klemes, The spectral type of the staircase transformation, 1993, preprint.
  • [KR] I. Klemes and K. Rheinhold, Rank-one tranformations with singular spectral type, Israel J. Math. (1995), to appear.
  • [O] D. Ornstein, On the Root Problem in Ergodic Theory, Proc. of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Univ. of California Press, 1972, pp. 347-356. MR 53:3259
  • [R] V.V. Ryzhikov, Joinings and multiple mixing of the actions of finite rank, Funkts. Anal. i Ego Pril. 27 (1993), 63-78, in Russian. MR 95a:28016

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 28D05

Retrieve articles in all journals with MSC (1991): 28D05

Additional Information

Terrence M. Adams
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250
Address at time of publication: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210-1174

Keywords: Mixing, rank-1
Received by editor(s): August 20, 1996
Communicated by: Mary Rees
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society