NUMERICAL COMPUTATION OF DICHOTOMY RATES AND PROJECTORS IN DISCRETE TIME

Hüls T (2009)
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 12(1): 109-131.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We introduce a characterization of exponential dichotomies for linear difference equations that can be tested numerically and enables the approximation of dichotomy rates and projectors with high accuracy. The test is based on computing the bounded solutions of a specific inhomogeneous difference equation. For this task a boundary value and a least squares approach is applied. The results are illustrated using Henon's map. We compute approximations of dichotomy rates and projectors of the variational equation, along a homoclinic orbit and an orbit on the attractor as well as for an almost periodic example. For the boundary value and the least squares approach, we analyze in detail errors that occur, when restricting the infinite dimensional problem to a finite interval.
Stichworte
Dichotomy projectors; Exponential dichotomy; Boundary value problem; Least squares solution
Erscheinungsjahr
2009
Zeitschriftentitel
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Band
12
Ausgabe
1
Seite(n)
109-131
ISSN
1531-3492
Page URI
https://pub.uni-bielefeld.de/record/1633778

Zitieren

Hüls T. NUMERICAL COMPUTATION OF DICHOTOMY RATES AND PROJECTORS IN DISCRETE TIME. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B. 2009;12(1):109-131.
Hüls, T. (2009). NUMERICAL COMPUTATION OF DICHOTOMY RATES AND PROJECTORS IN DISCRETE TIME. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 12(1), 109-131. https://doi.org/10.3934/dcdsb.2009.12.109
Hüls, T. (2009). NUMERICAL COMPUTATION OF DICHOTOMY RATES AND PROJECTORS IN DISCRETE TIME. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 12, 109-131.
Hüls, T., 2009. NUMERICAL COMPUTATION OF DICHOTOMY RATES AND PROJECTORS IN DISCRETE TIME. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 12(1), p 109-131.
T. Hüls, “NUMERICAL COMPUTATION OF DICHOTOMY RATES AND PROJECTORS IN DISCRETE TIME”, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 12, 2009, pp. 109-131.
Hüls, T.: NUMERICAL COMPUTATION OF DICHOTOMY RATES AND PROJECTORS IN DISCRETE TIME. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B. 12, 109-131 (2009).
Hüls, Thorsten. “NUMERICAL COMPUTATION OF DICHOTOMY RATES AND PROJECTORS IN DISCRETE TIME”. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 12.1 (2009): 109-131.

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