Angular spectra of linear dynamical systems in discrete time
Beyn W-J, Hüls T (2024)
Discrete and Continuous Dynamical Systems. Series B.
Zeitschriftenaufsatz
| E-Veröff. vor dem Druck | Englisch
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Einrichtung
Abstract / Bemerkung
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between successive subspaces generated by the dynamical system. The angular spectrum is bounded by angular values which have previously been investigated by the authors. In this contribution we derive explicit formulas for the angular spectrum of some autonomous and specific nonautonomous systems. Based on a reduction principle we set up a numerical method for the general case; we investigate its convergence and apply the method to systems with a homoclinic orbit and a strange attractor. Our main theoretical result is a theorem on the invariance of the angular spectrum under summable perturbations of the given matrices (roughness theorem). It applies to systems with a so-called complete exponential dichotomy (CED), a concept which we introduce in this paper and which imposes more stringent conditions than those underlying the exponential dichotomy spectrum.
Stichworte
KeNonautonomous dynamical systems;
angular spectrum;
ergodic aver;
age;
roughness theorems;
Sacker-Sell spectrum;
numerical approximation.
Erscheinungsjahr
2024
Zeitschriftentitel
Discrete and Continuous Dynamical Systems. Series B
ISSN
1531-3492
eISSN
1553-524X
Page URI
https://pub.uni-bielefeld.de/record/2989928
Zitieren
Beyn W-J, Hüls T. Angular spectra of linear dynamical systems in discrete time. Discrete and Continuous Dynamical Systems. Series B. 2024.
Beyn, W. - J., & Hüls, T. (2024). Angular spectra of linear dynamical systems in discrete time. Discrete and Continuous Dynamical Systems. Series B. https://doi.org/10.3934/dcdsb.2024144
Beyn, Wolf-Jürgen, and Hüls, Thorsten. 2024. “Angular spectra of linear dynamical systems in discrete time”. Discrete and Continuous Dynamical Systems. Series B.
Beyn, W. - J., and Hüls, T. (2024). Angular spectra of linear dynamical systems in discrete time. Discrete and Continuous Dynamical Systems. Series B.
Beyn, W.-J., & Hüls, T., 2024. Angular spectra of linear dynamical systems in discrete time. Discrete and Continuous Dynamical Systems. Series B.
W.-J. Beyn and T. Hüls, “Angular spectra of linear dynamical systems in discrete time”, Discrete and Continuous Dynamical Systems. Series B, 2024.
Beyn, W.-J., Hüls, T.: Angular spectra of linear dynamical systems in discrete time. Discrete and Continuous Dynamical Systems. Series B. (2024).
Beyn, Wolf-Jürgen, and Hüls, Thorsten. “Angular spectra of linear dynamical systems in discrete time”. Discrete and Continuous Dynamical Systems. Series B (2024).
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Preprint: 10.48550/ARXIV.2404.02694
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