Smorodinsky’s conjecture on rank-one mixing

Adams, Terrence

doi:10.1090/S0002-9939-98-04082-9

Smorodinsky’s conjecture on rank-one mixing
HTML articles powered by AMS MathViewer

by Terrence M. Adams PDF

Proc. Amer. Math. Soc. 126 (1998), 739-744 Request permission

Abstract:

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

References

T.M. Adams and N.A. Friedman, Staircase mixing, Ergod. Th. & Dynam. Sys., to appear.
J. R. Blum and D. L. Hanson, On the mean ergodic theorem for subsequences, Bull. Amer. Math. Soc. 66 (1960), 308–311. MR 118803, DOI 10.1090/S0002-9904-1960-10481-8
J. R. Choksi and M. G. Nadkarni, The maximal spectral type of a rank one transformation, Canad. Math. Bull. 37 (1994), no. 1, 29–36. MR 1261554, DOI 10.4153/CMB-1994-005-4
Nathaniel A. Friedman, Introduction to ergodic theory, Van Nostrand Reinhold Mathematical Studies, No. 29, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1970. MR 0435350
Nathaniel A. Friedman, Mixing on sequences, Canad. J. Math. 35 (1983), no. 2, 339–352. MR 695088, DOI 10.4153/CJM-1983-019-2
Steven Arthur Kalikow, Twofold mixing implies threefold mixing for rank one transformations, Ergodic Theory Dynam. Systems 4 (1984), no. 2, 237–259. MR 766104, DOI 10.1017/S014338570000242X
Jonathan L. King, Joining-rank and the structure of finite rank mixing transformations, J. Analyse Math. 51 (1988), 182–227. MR 963154, DOI 10.1007/BF02791123
I. Klemes, The spectral type of the staircase transformation, 1993, preprint.
I. Klemes and K. Rheinhold, Rank-one tranformations with singular spectral type, Israel J. Math. (1995), to appear.
Donald S. Ornstein, On the root problem in ergodic theory, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 347–356. MR 0399415
V. V. Ryzhikov, Joinings and multiple mixing of the actions of finite rank, Funktsional. Anal. i Prilozhen. 27 (1993), no. 2, 63–78, 96 (Russian, with Russian summary); English transl., Funct. Anal. Appl. 27 (1993), no. 2, 128–140. MR 1251168, DOI 10.1007/BF01085983