Mixing rank-one actions of locally compact abelian groups

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1. [1] T.M. Adams, Smorodinsky's conjecture on rank one systems, Proc. Amer. Math. Soc.126 (1998) 739-744. Zbl0906.28006MR1443143
2. [2] T.M. Adams, N.A. Friedman, Staircase mixing, preprint, 1992. 
3. [3] T. Adams, C.E. Silva, $Z^d$-staircase actions, Ergodic Theory Dynam. Systems19 (1999) 837-850. Zbl0939.28013MR1709423
4. [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. Zbl0846.05095
5. [5] D. Creutz, C.E. Silva, Mixing on a class of rank-one transformations, Ergodic Theory Dynam. Systems24 (2004) 407-440. Zbl1066.37003MR2054050
6. [6] A.I. Danilenko, Funny rank one weak mixing for nonsingular Abelian actions, Israel J. Math.121 (2001) 29-54. Zbl1024.28014MR1818379
7. [7] A.I. Danilenko, Infinite rank one actions and nonsingular Chacon transformations, Illinois J. Math.48 (2004) 769-786. Zbl1069.37003MR2114251
8. [8] A.I. Danilenko, Mixing rank-one actions for infinite sums of finite groups, Israel J. Math.156 (2006) 341-358. Zbl1131.37006MR2282382
9. [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. Zbl1061.37003MR2025335
10. [10] A. del Junco, A simple map with no prime factors, Israel J. Math.104 (1998) 301-320. Zbl0915.28011MR1622315
11. [11] A. del Junco, R. Yassawi, Multiple mixing rank one group actions, Canad. J. Math.52 (2000) 332-347. Zbl0957.28008MR1755781
12. [12] B. Fayad, Rank one and mixing differentiable flows, Invent. Math.160 (2005) 305-340. Zbl1064.37006MR2138069
13. [13] C. Hoffman, A loosely Bernoulli counterexample machine, Israel J. Math.112 (1999) 237-247. Zbl0943.37003MR1714994
14. [14] S.A. Kalikow, Twofold mixing implies threefold mixing for rank one transformations, Ergodic Theory Dynam. Systems4 (1984) 237-259. Zbl0552.28016MR766104
15. [15] J.L. King, Joining-rank and the structure of finite rank mixing transformations, J. Analyse Math.51 (1988) 182-227. Zbl0665.28010MR963154
16. [16] A. Leibman, Polynomial mappings of groups, Israel J. Math.129 (2002) 29-60. Zbl1007.20035MR1910931
17. [17] B. Madore, Rank-one group actions with simple mixing $Z$-subactions, New York J. Math.10 (2004) 175-194. Zbl1074.37003MR2114785
18. [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. Zbl0262.28009MR399415
19. [19] A. Prikhodko, Stochastic constructions of flows of rank one, Mat. Sb.192 (2001) 61-92. Zbl1017.37002MR1885913
20. [20] D.J. Rudolph, The second centralizer of a Bernoulli shift is just its powers, Israel J. Math.29 (1978) 167-178. Zbl0375.28006MR485401
21. [21] D.J. Rudolph, An example of a measure preserving map with minimal self-joinings, J. Analyse Math.35 (1979) 97-122. Zbl0446.28018MR555301
22. [22] V.V. Ryzhikov, Mixing, rank and minimal self-joining of actions with invariant measure, Mat. Sb.183 (1992) 133-160. Zbl0768.28008MR1180921
23. [23] V.V. Ryzhikov, Joinings and multiple mixing of the actions of finite rank, Funktsional. Anal. i Prilozhen.27 (1993) 63-78. Zbl0853.28011MR1251168
24. [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. Zbl0957.28009MR1756740