Topological Methods in Nonlinear Analysis

Three zutot

Eli Glasner and Benjamin Weiss

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 49, Number 1 (2017), 351-358.

Dates
First available in Project Euclid: 11 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1491876033

Digital Object Identifier
doi:10.12775/TMNA.2016.084

Mathematical Reviews number (MathSciNet)
MR3635649

Zentralblatt MATH identifier
1379.37020

Citation

Glasner, Eli; Weiss, Benjamin. Three zutot. Topol. Methods Nonlinear Anal. 49 (2017), no. 1, 351--358. doi:10.12775/TMNA.2016.084. https://projecteuclid.org/euclid.tmna/1491876033


Export citation

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.
  • ––––, 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.
  • ––––, Minimal models for free actions, Dynamical Systems and Group Actions, 249–264, Contemp. Math. 567, Amer. Math. Soc., Providence, 2012.