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2000 | 84/85 | 2 | 345-361
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### Locally equicontinuous dynamical systems

Autorzy
Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
A new class of dynamical systems is defined, the class of "locally equicontinuous systems" (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in $l_{∞}(ℤ)$ form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems. Both of these inclusions are proper. The main result of the paper is to produce a family of examples of LE dynamical systems which are not WAP.
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Czasopismo
---
Rocznik
Tom
Numer
Strony
345-361
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-08-13
poprawiono
1999-10-19
Twórcy
autor
• Mathematics Department, Tel Aviv University, Tel Aviv, Israel
autor
• Mathematics Institute, Hebrew University of Jerusalem, Jerusalem, Israel
Bibliografia
• [AAB1] E. Akin, J. Auslander and K. Berg, When is a transitive map chaotic, in: Convergence in Ergodic Theory and Probability Walter de Gruyter, 1996, 25-40.
• [AAB2] E. Akin, J. Auslander and K. Berg, Almost equicontinuity and the enveloping semigroup, in: Topological Dynamics and Applications (Minneapolis, MN, 1995), Contemp. Math. 215, Amer. Math. Soc., Providence, RI, 1998, 75-81.
• [D] T. Downarowicz, Weakly almost periodic flows and hidden eigenvalues, in: Contemp. Math. 215, Amer. Math. Soc., 1998, 101-120.
• [EN] R. Ellis and M. Nerurkar, Weakly almost periodic flows, Trans. Amer. Math. Soc. 313 (1989), 103-119.
• [F1] H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation, Math. Systems Theory 1 (1967), 1-55.
• [F2] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton Univ. Press, Princeton, NJ, 1981.
• [GM] S. Glasner and D. Maon, Rigidity in topological dynamics, Ergodic Theory Dynam. Systems 9 (1989), 309-320.
• [GW] E. Glasner and B. Weiss, Sensitive dependence on initial conditions, Nonlinearity 6 (1993), 1067-1075.
• [HR] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I, Springer, Berlin, 1963.
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Bibliografia
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