Homoclinic trajectories of non-autonomous maps

Hüls T (2011)
Journal of Difference Equations and Applications 17(1): 9-31.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
For non-autonomous difference equations of the form[image omitted]we consider homoclinic trajectories. These are pairs of trajectories that converge in both time directions towards each other. Assuming hyperbolicity, we derive a numerical method to compute homoclinic trajectories in two steps. In the first step, one trajectory is approximated by the solution of a boundary value problem and precise error estimates are given. In particular, influences of parameters [image omitted] with vertical bar n vertical bar large are discussed in detail. A second trajectory that is homoclinic to the first one is computed in a subsequent step as follows. We transform the original system into a topologically equivalent form having 0 as an n-independent fixed point. Applying the boundary value ansatz to the transformed system, we obtain a non-autonomous homoclinic orbit, converging towards the origin (T. Huls, J. Difference Equ. Appl. 12(11) (2006), pp. 1103-1126). Transforming back to the original coordinates leads to the desired homoclinic trajectories. The numerical method and the validity of the error estimates are illustrated by examples.
Stichworte
error analysis; numerical approximation; trajectories; homoclinic; non-autonomous discrete time dynamical systems
Erscheinungsjahr
2011
Zeitschriftentitel
Journal of Difference Equations and Applications
Band
17
Ausgabe
1
Seite(n)
9-31
ISSN
1023-6198
Page URI
https://pub.uni-bielefeld.de/record/1967969

Zitieren

Hüls T. Homoclinic trajectories of non-autonomous maps. Journal of Difference Equations and Applications. 2011;17(1):9-31.
Hüls, T. (2011). Homoclinic trajectories of non-autonomous maps. Journal of Difference Equations and Applications, 17(1), 9-31. https://doi.org/10.1080/10236190902932742
Hüls, T. (2011). Homoclinic trajectories of non-autonomous maps. Journal of Difference Equations and Applications 17, 9-31.
Hüls, T., 2011. Homoclinic trajectories of non-autonomous maps. Journal of Difference Equations and Applications, 17(1), p 9-31.
T. Hüls, “Homoclinic trajectories of non-autonomous maps”, Journal of Difference Equations and Applications, vol. 17, 2011, pp. 9-31.
Hüls, T.: Homoclinic trajectories of non-autonomous maps. Journal of Difference Equations and Applications. 17, 9-31 (2011).
Hüls, Thorsten. “Homoclinic trajectories of non-autonomous maps”. Journal of Difference Equations and Applications 17.1 (2011): 9-31.

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