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August  2007, 17(3): 561-587. doi: 10.3934/dcds.2007.17.561

Morse decomposition of semiflows on fiber bundles

Mauro Patrão 1, and  Luiz A. B. San Martin 1,

1. 

Instituto de Matemática, Universidade Estadual de Campinas, Cx. Postal 6065, 13.081-970 Campinas-SP, Brazil, Brazil

Received  January 2006 Revised  August 2006 Published  December 2006

We study chain transitivity and Morse decompositions of discrete and continuous-time semiflows on fiber bundles with emphasis on (generalized) flag bundles. In this case an algebraic description of the chain transitive sets is given. Our approach consists in embedding the semiflow in a semigroup of continuous maps to take advantage of the good properties of the semigroup actions on the flag manifolds.
Keywords: Chain transitivity, Morse decomposition., semi-simple Lie groups, semiflows, flag manifolds, fiber bundles, semigroups.
Mathematics Subject Classification: Primary: 37B05, 37B35. Secondary: 20M20, 22E4.
Citation: Mauro Patrão, Luiz A. B. San Martin. Morse decomposition of semiflows on fiber bundles. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 561-587. doi: 10.3934/dcds.2007.17.561
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