Lyapunov stability on fiber bundles

In this paper we develop a theory of Lyapunov stability for generalized flows on principal and associated bundles. We present a study of Lyapunov stability and attraction in the total space of a principal bundle by means of the action of the structure group.We also relate limit sets, prolongations,...

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Veröffentlicht in:	Boletim da Sociedade Brasileira de Matemática 2015-06, Vol.46 (2), p.181-204
Hauptverfasser:	Barros, Carlos J. Braga, Souza, Josiney A., Rocha, Victor H. L.
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	In this paper we develop a theory of Lyapunov stability for generalized flows on principal and associated bundles. We present a study of Lyapunov stability and attraction in the total space of a principal bundle by means of the action of the structure group.We also relate limit sets, prolongations, prolongational limit sets, attracting sets and stable sets in the total space of an associated bundle to the corresponding concepts in the fibers.
ISSN:	1678-7544 1678-7714
DOI:	10.1007/s00574-015-0090-1