COMPUTING STABLE HIERARCHIES OF FIBER BUNDLES

Hüls T (2017)
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 22(9): 3341-3367.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Stable fiber bundles are important structures for understanding nonautonomous dynamics. These sets have a hierarchical structure ranging from stable to strong stable fibers. First, we compute corresponding structures for linear systems and prove an error estimate. The spectral concept of choice is the Sacker-Sell spectrum that is based on exponential dichotomies. Secondly, we tackle the nonlinear case and propose an algorithm for the numerical approximation of stable hierarchies in nonautonomous difference equations. This method generalizes the contour algorithm for computing stable fibers from [38, 39]. It is based on Hadamard's graph transform and approximates fibers of the hierarchy by zero-contours of specific operators. We calculate fiber bundles and illustrate errors involved for several examples, including a nonautonomous Lorenz model.
Stichworte
Hierarchy of invariant fiber bundles; dynamical systems; noninvertible; and nonautonomous dynamics; numerical approximation; contour algorithm
Erscheinungsjahr
2017
Zeitschriftentitel
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Band
22
Ausgabe
9
Seite(n)
3341-3367
ISSN
1531-3492
eISSN
1553-524X
Page URI
https://pub.uni-bielefeld.de/record/2916443

Zitieren

Hüls T. COMPUTING STABLE HIERARCHIES OF FIBER BUNDLES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B. 2017;22(9):3341-3367.
Hüls, T. (2017). COMPUTING STABLE HIERARCHIES OF FIBER BUNDLES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 22(9), 3341-3367. https://doi.org/10.3934/dcdsb.2017140
Hüls, T. (2017). COMPUTING STABLE HIERARCHIES OF FIBER BUNDLES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 22, 3341-3367.
Hüls, T., 2017. COMPUTING STABLE HIERARCHIES OF FIBER BUNDLES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 22(9), p 3341-3367.
T. Hüls, “COMPUTING STABLE HIERARCHIES OF FIBER BUNDLES”, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 22, 2017, pp. 3341-3367.
Hüls, T.: COMPUTING STABLE HIERARCHIES OF FIBER BUNDLES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B. 22, 3341-3367 (2017).
Hüls, Thorsten. “COMPUTING STABLE HIERARCHIES OF FIBER BUNDLES”. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 22.9 (2017): 3341-3367.

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