Abstract
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.
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Research supported by Fundação Araucária conv. 472/2014 and 476/2014, and CNPq 476024/2012-9 Universal 14/2012.
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Barros, C.J.B., Souza, J.A. & Rocha, V.H.L. Lyapunov stability on fiber bundles. Bull Braz Math Soc, New Series 46, 181–204 (2015). https://doi.org/10.1007/s00574-015-0090-1
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DOI: https://doi.org/10.1007/s00574-015-0090-1