Some remarks about strong proximality of compact flows

Tom 115 / 2009

A. Bouziad, J.-P. Troallic Colloquium Mathematicum 115 (2009), 159-170 MSC: 54H20, 60B05. DOI: 10.4064/cm115-2-2

Streszczenie

This note aims at providing some information about the concept of a strongly proximal compact transformation semigroup. In the affine case, a unified approach to some known results is given. It is also pointed out that a compact flow $(X, {\mathcal S})$ is strongly proximal if (and only if) it is proximal and every point of $X$ has an ${\mathcal S}$-strongly proximal neighborhood in $X$. An essential ingredient, in the affine as well as in the nonaffine case, turns out to be the existence of a unique minimal subset.

Autorzy

  • A. BouziadUMR CNRS 6085
    Département de Mathématiques
    Université de Rouen
    Avenue de l'Université B.P. 12
    F-76801 Saint Etienne
    du Rouvray, France
    e-mail
  • J.-P. TroallicUMR CNRS 6085
    UFR des Sciences et Techniques
    Université du Havre
    25 rue Philippe Lebon, B.P. 540
    F-76058 Le Havre Cedex, France
    e-mail

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