Geodesic
Some remarks about strong proximality of compact flows
A. Bouziad1 ; J.-P. Troallic2
1UMR CNRS 6085 Département de Mathématiques Université de Rouen Avenue de l'Université B.P. 12 F-76801 Saint Etienne du Rouvray, France
2UMR CNRS 6085 UFR des Sciences et Techniques Université du Havre 25 rue Philippe Lebon, B.P. 540 F-76058 Le Havre Cedex, France
Colloquium Mathematicum, Tome 115 (2009) no. 2, pp. 159-170
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm115-2-2
Keywords: note aims providing information about concept strongly proximal compact transformation semigroup affine unified approach known results given pointed out compact flow mathcal strongly proximal only proximal every point has mathcal strongly proximal neighborhood essential ingredient affine nonaffine turns out existence unique minimal subset

A. Bouziad  1   ; J.-P. Troallic  2

1 UMR CNRS 6085 Département de Mathématiques Université de Rouen Avenue de l'Université B.P. 12 F-76801 Saint Etienne du Rouvray, France
2 UMR CNRS 6085 UFR des Sciences et Techniques Université du Havre 25 rue Philippe Lebon, B.P. 540 F-76058 Le Havre Cedex, France 
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A. Bouziad; J.-P. Troallic. Some remarks about strong proximality of compact flows. Colloquium Mathematicum, Tome 115 (2009) no. 2, pp. 159-170. doi: 10.4064/cm115-2-2

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