Mixing rank-one actions of locally compact abelian groups
Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 4, pp. 375-398.
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     title = {Mixing rank-one actions of locally compact abelian groups},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {375--398},
     publisher = {Elsevier},
     volume = {43},
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     doi = {10.1016/j.anihpb.2006.05.002},
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     zbl = {1126.37004},
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     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2006.05.002/}
}
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Danilenko, Alexandre I.; Silva, Cesar E. Mixing rank-one actions of locally compact abelian groups. Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 4, pp. 375-398. doi : 10.1016/j.anihpb.2006.05.002. http://archive.numdam.org/articles/10.1016/j.anihpb.2006.05.002/

[1] T.M. Adams, Smorodinsky's conjecture on rank one systems, Proc. Amer. Math. Soc. 126 (1998) 739-744. | MR | Zbl

[2] T.M. Adams, N.A. Friedman, Staircase mixing, preprint, 1992.

[3] T. Adams, C.E. Silva, Z d -staircase actions, Ergodic Theory Dynam. Systems 19 (1999) 837-850. | MR | Zbl

[4] V. Bergelson, Ergodic Ramsey theory-an update, in: Ergodic Theory of Z d Actions, Warwick, 1993-1994, London Math. Soc. Lecture Note Ser., vol. 228, Cambridge Univ. Press, Cambridge, 1996, pp. 1-61. | Zbl

[5] D. Creutz, C.E. Silva, Mixing on a class of rank-one transformations, Ergodic Theory Dynam. Systems 24 (2004) 407-440. | MR | Zbl

[6] A.I. Danilenko, Funny rank one weak mixing for nonsingular Abelian actions, Israel J. Math. 121 (2001) 29-54. | MR | Zbl

[7] A.I. Danilenko, Infinite rank one actions and nonsingular Chacon transformations, Illinois J. Math. 48 (2004) 769-786. | MR | Zbl

[8] A.I. Danilenko, Mixing rank-one actions for infinite sums of finite groups, Israel J. Math. 156 (2006) 341-358. | MR | Zbl

[9] A.I. Danilenko, C.E. Silva, Multiple and polynomial recurrence for Abelian actions in infinite measure, J. London Math. Soc. (2) 69 (2004) 183-200. | MR | Zbl

[10] A. Del Junco, A simple map with no prime factors, Israel J. Math. 104 (1998) 301-320. | MR | Zbl

[11] A. Del Junco, R. Yassawi, Multiple mixing rank one group actions, Canad. J. Math. 52 (2000) 332-347. | MR | Zbl

[12] B. Fayad, Rank one and mixing differentiable flows, Invent. Math. 160 (2005) 305-340. | MR | Zbl

[13] C. Hoffman, A loosely Bernoulli counterexample machine, Israel J. Math. 112 (1999) 237-247. | MR | Zbl

[14] S.A. Kalikow, Twofold mixing implies threefold mixing for rank one transformations, Ergodic Theory Dynam. Systems 4 (1984) 237-259. | MR | Zbl

[15] J.L. King, Joining-rank and the structure of finite rank mixing transformations, J. Analyse Math. 51 (1988) 182-227. | MR | Zbl

[16] A. Leibman, Polynomial mappings of groups, Israel J. Math. 129 (2002) 29-60. | MR | Zbl

[17] B. Madore, Rank-one group actions with simple mixing Z-subactions, New York J. Math. 10 (2004) 175-194. | MR | Zbl

[18] D.S. Ornstein, On the root problem in ergodic theory, in: Proc. Sixth Berkeley Symp. Math. Stat. Prob. vol. II, Univ. California, Berkeley, CA, 1970/1971, Univ. of California Press, Berkeley, CA, 1972, pp. 347-356. | MR | Zbl

[19] A. Prikhodko, Stochastic constructions of flows of rank one, Mat. Sb. 192 (2001) 61-92. | MR | Zbl

[20] D.J. Rudolph, The second centralizer of a Bernoulli shift is just its powers, Israel J. Math. 29 (1978) 167-178. | MR | Zbl

[21] D.J. Rudolph, An example of a measure preserving map with minimal self-joinings, J. Analyse Math. 35 (1979) 97-122. | MR | Zbl

[22] V.V. Ryzhikov, Mixing, rank and minimal self-joining of actions with invariant measure, Mat. Sb. 183 (1992) 133-160. | MR | Zbl

[23] V.V. Ryzhikov, Joinings and multiple mixing of the actions of finite rank, Funktsional. Anal. i Prilozhen. 27 (1993) 63-78. | MR | Zbl

[24] V.V. Ryzhikov, The Rokhlin problem on multiple mixing in the class of actions of positive local rank, Funktsional. Anal. i Prilozhen. 34 (2000) 90-93. | MR | Zbl

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