All-time Morse decompositions of linear nonautonomous dynamical systems
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- by Martin Rasmussen
- Proc. Amer. Math. Soc. 136 (2008), 1045-1055
- DOI: https://doi.org/10.1090/S0002-9939-07-09071-5
- Published electronically: November 28, 2007
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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.References
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Bibliographic Information
- Martin Rasmussen
- Affiliation: Department of Mathematics, University of Augsburg, D-86135 Augsburg, Germany
- MR Author ID: 751819
- Email: martin.rasmussen@math.uni-augsburg.de
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 1045-1055
- MSC (2000): Primary 34D05, 37B25, 37B55, 37C70, 39A11
- DOI: https://doi.org/10.1090/S0002-9939-07-09071-5
- MathSciNet review: 2361880