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On the number of maximal chain transitive sets in fiber bundles
-
Carlos J. Braga Barros
and
Josiney A. Souza
Published/Copyright:
March 1, 2013
Abstract.
This article studies chain transitivity for semigroup actions on fiber bundles whose typical fibers are compact topological spaces. We discuss the number of maximal chain transitive sets and, as a consequence, we obtain conditions for the existence of a finest Morse decomposition. Some of the results obtained are applied to orthonormal frame and Stiefel manifolds. A description of the maximal chain transitive sets is provided in terms of the action of shadowing semigroups. This description is well known in the literature under the hypothesis of local transitivity. Here, we exclude the hypothesis of local transitivity when the state space is a compact quotient space of a topological group.
Keywords: Semigroup actions; chain transitivity; chain transitive sets; fiber bundles; homogeneous spaces
Received: 2010-04-27
Revised: 2011-02-20
Published Online: 2013-03-01
Published in Print: 2013-03-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Semigroup actions;
chain transitivity;
chain transitive sets;
fiber bundles;
homogeneous spaces
Articles in the same Issue
- Masthead
- Non-Lipschitz flow of the nonlinear Schrödinger equation on surfaces
- Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary
- A composite map in the stable homotopy groups of spheres
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- On the Eisenstein cohomology of odd orthogonal groups
- Complex Osserman Kähler manifolds in dimension four
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- On the number of maximal chain transitive sets in fiber bundles
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- Imprecise probabilities, bets and functional analytic methods in Łukasiewicz logic
