Three zutot
Keywords
Product recurrence, double minimality, uniform rigidity, measure weak mixing, strict ergodicity, amenabilityAbstract
Three topics in dynamical systems are discussed. First we deal with cascades and solve two open problems concerning, respectively, product recurrence, and uniformly rigid actions. Next we provide a new example that displays some unexpected properties of strictly ergodic actions of non-amenable groups.References
E. Akin and S. Kolyada, Li–Yorke sensitivity, Nonlinearity 16 (2003), 1421–1433.
J. Auslander and H. Furstenberg, Product recurrence and distal points, Trans. Amer. Math. Soc. 343, (1994), no. 1, 221–232.
P. Dong, S. Shao and X. Ye, Product recurrent properties, disjointness and weak disjointness, Israel J. Math. 188 (2012), 463–507.
H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton University Press, Princeton, 1981.
H. Furstenberg, H. Keynes and L. Shapiro, Prime flows in topological dynamics, Israel J. Math. 14 (1973), 26–38.
H. Furstenberg and B. Weiss, On almost 1–1 extensions, Israel J. Math. 65 (1989), 311–322.
E. Glasner, Ergodic Theory via Joinings, Math. Surveys Monogr. 101, Amer. Math. Soc., Providence, 2003.
E. Glasner and D. Maon, Rigidity in topological dynamics, Ergodic Theory Dynam. Systems 9 (1989), 309–320.
E. Glasner and B. Weiss, On the construction of minimal skew products, Israel J. Math. 34 (1979), 321–336.
E. Glasner and B. Weiss, A weakly mixing upside-down tower of isometric extensions, Ergodic Theory Dynam. Systems 1 (1981), 151–157.
K. Haddad and W. Ott, Recurrence in pairs, Ergodic Theory Dynam. Systems 28 (2008), 1135–1143.
J. James, T. Koberda, K. Lindsey, C.E. Silva and P. Speh, On ergodic transformations that are both weakly mixing and uniformly rigid, New York J. Math. 15 (2009), 393–403.
J.L. King, A map with topological minimal self-joinings in the sense of del Junco, Ergodic Theory Dynam. Systems 10 (1990), 745–761.
B. Weiss, Multiple recurrence and doubly minimal systems, Topological Dynamics and Applications (Minneapolis, 1995), 189–196, Contemp. Math. 215, Amer. Math. Soc., Providence, 1998.
B. Weiss, Minimal models for free actions, Dynamical Systems and Group Actions, 249–264, Contemp. Math. 567, Amer. Math. Soc., Providence, 2012.
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 0
Number of citations: 0