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2000 | 84/85 | 1 | 83-94
Tytuł artykułu

Stretching the Oxtoby-Ulam Theorem

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
On a manifold X of dimension at least two, let μ be a nonatomic measure of full support with μ(∂X) = 0. The Oxtoby-Ulam Theorem says that ergodicity of μ is a residual property in the group of homeomorphisms which preserve μ. Daalderop and Fokkink have recently shown that density of periodic points is residual as well. We provide a proof of their result which replaces the dependence upon the Annulus Theorem by a direct construction which assures topologically robust periodic points.
Słowa kluczowe
Rocznik
Tom
Numer
1
Strony
83-94
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-05-20
poprawiono
2000-02-18
Twórcy
autor
  • Mathematics Department, The City College, 137 Street and Convent Avenue, New York, NY 10031, U.S.A.
Bibliografia
  • [1] E. Akin, The General Topology of Dynamical Systems, Amer. Math. Soc., Providence, 1993.
  • [2] S. Alpern and V. Prasad, Typical properties of volume preserving homeomorphisms, to appear (2000).
  • [3] J. Banks, Regular periodic decompositions for topologically transitive maps, Ergodic Theory Dynam. Systems 17 (1997), 505-529.
  • [4] F. Daalderop and R. Fokkink, Chaotic homeomorphisms are generic, Topology Appl., to appear (2000).
  • [5] J. Milnor, Topology from the Differentiable Viewpoint, Univ. of Virginia Press, Charlottesville, VA, 1965.
  • [6] Z. Nitecki and M. Shub, Filtrations, decompositions, and explosions, Amer. J. Math. 97 (1975), 1029-1047.
  • [7] J. Oxtoby, Note on transitive transformations, Proc. Nat. Acad. Sci. U.S.A. 23 (1937), 443-446.
  • [8] J. Oxtoby, Diameters of arcs and the gerrymandering problem, Amer. Math. Monthly 84 (1977), 155-162.
  • [9] J. Oxtoby, Measure and Category, 2nd ed., Springer, New York, NY, 1980.
  • [10] J. Oxtoby and S. Ulam, Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941), 874-920.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv84i1p83bwm
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