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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Smorodinsky's conjecture on rank-one mixing

Author(s): Terrence M. Adams
Journal: Proc. Amer. Math. Soc. 126 (1998), 739-744.
MSC (1991): Primary 28D05
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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:

[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


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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
Email: tadams@math.unc.edu, tadams@math.ohio-state.edu

DOI: 10.1090/S0002-9939-98-04082-9
PII: S 0002-9939(98)04082-9
Keywords: Mixing, rank-1
Received by editor(s): August 20, 1996
Communicated by: Mary Rees
Copyright of article: Copyright 1998, American Mathematical Society


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