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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

All-time Morse decompositions of linear nonautonomous dynamical systems


Author: Martin Rasmussen
Journal: Proc. Amer. Math. Soc. 136 (2008), 1045-1055
MSC (2000): Primary 34D05, 37B25, 37B55, 37C70, 39A11
Published electronically: November 28, 2007
MathSciNet review: 2361880
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Abstract: Morse decompositions provide inside information about the global asymptotic behavior of dynamical systems on compact metric spaces. Recently, the existence of Morse decompositions for nonautonomous dynamical systems was proved by restricting attention to the past or the future of the system, but in general, such a construction is not realizable for the entire time. In this article, it is shown that all-time Morse decompositions can be defined for linear systems on the projective space. Moreover, the dynamical properties are discussed and an analogue to the Theorem of Selgrade is proved.


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Additional Information

Martin Rasmussen
Affiliation: Department of Mathematics, University of Augsburg, D-86135 Augsburg, Germany
Email: martin.rasmussen@math.uni-augsburg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09071-5
PII: S 0002-9939(07)09071-5
Keywords: Attractor, attractor-repeller pair, Morse decomposition, Morse set, nonautonomous dynamical system, projective space, repeller
Received by editor(s): July 11, 2006
Received by editor(s) in revised form: January 16, 2007
Published electronically: November 28, 2007
Additional Notes: Research supported by Bayerisches Eliteförderungsgesetz of the State of Bavaria, Germany
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2007 American Mathematical Society