### Angular values of linear dynamical systems and their connection to the dichotomy spectrum

Beyn W-J, Hüls T (2020)
arXiv:2012.11340.

Preprint | Englisch

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Abstract / Bemerkung
This work continues the investigation of the previously defined angular values for linear nonautonomous dynamical systems in finite dimensions. The $s$-th angular value measures the maximal average rotation which the dynamics exerts on $s$-dimensional subspaces. Our main theorem relates the angular values to the well-known dichotomy (or Sacker-Sell) spectrum and its associated spectral bundles. In particular, we prove a reduction theorem which shows that instead of general subspaces it suffices to consider so-called trace spaces which have their basis in the spectral fibers. The reduction leads to an algorithm for computing angular values of dimensions one and two. We apply the algorithm to several examples of dimension up to $4$, including a system of coupled oscillators.
Erscheinungsjahr
2020
Zeitschriftentitel
arXiv:2012.11340
Page URI
https://pub.uni-bielefeld.de/record/2955505

### Zitieren

Beyn W-J, Hüls T. Angular values of linear dynamical systems and their connection to the dichotomy spectrum. arXiv:2012.11340. 2020.
Beyn, W. - J., & Hüls, T. (2020). Angular values of linear dynamical systems and their connection to the dichotomy spectrum. arXiv:2012.11340
Beyn, W. - J., and Hüls, T. (2020). Angular values of linear dynamical systems and their connection to the dichotomy spectrum. arXiv:2012.11340.
Beyn, W.-J., & Hüls, T., 2020. Angular values of linear dynamical systems and their connection to the dichotomy spectrum. arXiv:2012.11340.
W.-J. Beyn and T. Hüls, “Angular values of linear dynamical systems and their connection to the dichotomy spectrum”, arXiv:2012.11340, 2020.
Beyn, W.-J., Hüls, T.: Angular values of linear dynamical systems and their connection to the dichotomy spectrum. arXiv:2012.11340. (2020).
Beyn, Wolf-Jürgen, and Hüls, Thorsten. “Angular values of linear dynamical systems and their connection to the dichotomy spectrum”. arXiv:2012.11340 (2020).

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### Quellen

arXiv: 2012.11340