Lyapunov and Sacker–Sell Spectral Intervals |
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Authors: | Luca Dieci Erik S Van Vleck |
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Institution: | (1) School of Mathematics, Georgia Institute of Technology, Atlanta, 30332, Georgia;(2) Department of Mathematics, University of Kansas, Lawrence, 66045, Kansas, USA |
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Abstract: | In this work, we show that for linear upper triangular systems of differential equations, we can use the diagonal entries
to obtain the Sacker and Sell, or Exponential Dichotomy, and also –under some restrictions– the Lyapunov spectral intervals. Since any bounded and continuous coefficient matrix function can be smoothly transformed to an upper
triangular matrix function, our results imply that these spectral intervals may be found from scalar homogeneous problems.
In line with our previous work Dieci and Van Vleck (2003), SIAM J. Numer. Anal. 40, 516–542], we emphasize the role of integral separation. Relationships between different spectra are shown, and examples
are used to illustrate the results and define types of coefficient matrix functions that lead to continuous Sacker–Sell spectrum
and/or continuous Lyapunov spectrum.
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Keywords: | Exponential dichotomy Sacker– Sell spectrum Lyapunov exponents integral separation |
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