Stretching the Oxtoby-Ulam Theorem
Akin, Ethan
Colloquium Mathematicae, Tome 84/85 (2000), p. 83-94 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:210811 
@article{bwmeta1.element.bwnjournal-article-cmv84i1p83bwm,
     author = {Ethan Akin},
     title = {Stretching the Oxtoby-Ulam Theorem},
     journal = {Colloquium Mathematicae},
     volume = {84/85},
     year = {2000},
     pages = {83-94},
     zbl = {0959.37004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p83bwm}
}

Akin, Ethan. Stretching the Oxtoby-Ulam Theorem. Colloquium Mathematicae, Tome 84/85 (2000) pp. 83-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p83bwm/

[000] [1] E. Akin, The General Topology of Dynamical Systems, Amer. Math. Soc., Providence, 1993. | Zbl 0781.54025

[001] [2] S. Alpern and V. Prasad, Typical properties of volume preserving homeomorphisms, to appear (2000). | Zbl 0970.37001

[002] [3] J. Banks, Regular periodic decompositions for topologically transitive maps, Ergodic Theory Dynam. Systems 17 (1997), 505-529. | Zbl 0921.54029

[003] [4] F. Daalderop and R. Fokkink, Chaotic homeomorphisms are generic, Topology Appl., to appear (2000). | Zbl 0977.54032

[004] [5] J. Milnor, Topology from the Differentiable Viewpoint, Univ. of Virginia Press, Charlottesville, VA, 1965.

[005] [6] Z. Nitecki and M. Shub, Filtrations, decompositions, and explosions, Amer. J. Math. 97 (1975), 1029-1047. | Zbl 0324.58015

[006] [7] J. Oxtoby, Note on transitive transformations, Proc. Nat. Acad. Sci. U.S.A. 23 (1937), 443-446. | Zbl 0017.13603

[007] [8] J. Oxtoby, Diameters of arcs and the gerrymandering problem, Amer. Math. Monthly 84 (1977), 155-162. | Zbl 0355.52007

[008] [9] J. Oxtoby, Measure and Category, 2nd ed., Springer, New York, NY, 1980. | Zbl 0435.28011

[009] [10] J. Oxtoby and S. Ulam, Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941), 874-920. | Zbl 0063.06074