Dichotomy spectra and Morse decompositions of linear nonautonomous differential equations |
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Authors: | Martin Rasmussen |
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Institution: | Department of Mathematics, Imperial College, London SW72AZ, United Kingdom |
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Abstract: | Recently, the existence of Morse decompositions for nonautonomous dynamical systems was shown for three different time domains: the past, the future and—in the linear case—the entire time. In this article, notions of exponential dichotomy are discussed with respect to the three time domains. It is shown that an exponential dichotomy gives rise to an attractor-repeller pair in the projective space, which is a building block of a Morse decomposition. Moreover, based on the notions of exponential dichotomy, dichotomy spectra are introduced, and it is proved that the corresponding spectral manifolds lead to Morse decompositions in the projective space. |
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Keywords: | 34D05 34D09 34D45 37B25 37B55 37C70 |
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