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2000 | 84/85 | 2 | 395-419
Tytuł artykułu

Construction of non-constant and ergodic cocycles

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on the "closure of coboundaries technique", whereas the second result is proved by developing in addition a new approximation technique.
Słowa kluczowe
Rocznik
Tom
Numer
2
Strony
395-419
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-08-20
poprawiono
2000-02-02
Twórcy
  • Department of Mathematics, Rutgers University, Camden, NJ 08102, U.S.A.
Bibliografia
  • [AK] D. Anosov and A. Katok, New examples in smooth ergodic theory, Trans. Moscow Math. Soc. 23 (1970), 1-35.
  • [GM] S. Glasner and D. Maon, Rigidity in topological dynamics, Ergodic Theory Dynam. Systems 9 (1989), 309-320.
  • [GW] S. Glasner and B. Weiss, On the construction of minimal skew products, Israel J. Math. 34 (1979), 321-336.
  • [H] P. Halmos, Lectures on Ergodic Theory, Math. Soc. Japan, Tokyo, 1956.
  • [HSY] B. Hunt, T. Sauer and J. Yorke, Prevalence: A translation-invariant 'almost every' on infinite-dimensional spaces, Bull. Amer. Math. Soc. 27 (1992), 217-238.
  • [IS] A. Iwanik and J. Serafin, Most monothetic extensions are rank-1, Colloq. Math. 66 (1993), 63-76.
  • [JP] R. Jones and W. Parry, Compact abelian group extensions of dynamical systems II, Compositio Math. 25 (1972), 135-147.
  • [K] A. Katok, Constructions in Ergodic Theory, Part II, unpublished notes.
  • [M] I. Melbourne, Symmetric ω-limit sets for smooth Γ-equivariant dynamical systems with $Γ^0$ abelian, Nonlinearity 10 (1997), 1551-1567.
  • [N1] M. Nerurkar, Ergodic continuous skew product actions of amenable groups, Pacific J. Math. 119 (1985), 343-363.
  • [N2] M. Nerurkar, On the construction of smooth ergodic skew-products, Ergodic Theory Dynam. Systems 8 (1988), 311-326.
  • [Sch] K. Schmidt, Cocycles and Ergodic Transformation Groups, MacMillan of India, 1977.
  • [Z] R. Zimmer, Extensions of ergodic group actions, Illinois J. Math. 20 (1976), 373-409.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv84i2p395bwm
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