Homoclinic orbits of non-autonomous maps and their approximation

Hüls T (2006)
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS 12(11): 1103-1126.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We consider homoclinic orbits in non-autonomous discrete time dynamical systems of the form Xn+l = f(n)(x(n)), n is an element of Z, where it is assumed that an n independent fixed point exists. A numerical method for computing finite approximations of transversal homoclinic orbits is introduced and a detailed error analysis is presented. The non-autonomous setup requires special tools. We prove that the analytic condition of transversality of the orbit corresponds to a transversal intersection of the corresponding invariant fiber bundles. The approximation method and the validity of the error estimate is illustrated by an example.
Stichworte
homoclinic orbits; invariant fiber bundles; transversality; numerical; approximation; approximation error; non-autonomous; non-autonomous discrete time dynamical systems
Erscheinungsjahr
2006
Zeitschriftentitel
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
Band
12
Ausgabe
11
Seite(n)
1103-1126
ISSN
1023-6198
Page URI
https://pub.uni-bielefeld.de/record/1596680

Zitieren

Hüls T. Homoclinic orbits of non-autonomous maps and their approximation. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS. 2006;12(11):1103-1126.
Hüls, T. (2006). Homoclinic orbits of non-autonomous maps and their approximation. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 12(11), 1103-1126. https://doi.org/10.1080/10236190601045713
Hüls, T. (2006). Homoclinic orbits of non-autonomous maps and their approximation. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS 12, 1103-1126.
Hüls, T., 2006. Homoclinic orbits of non-autonomous maps and their approximation. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 12(11), p 1103-1126.
T. Hüls, “Homoclinic orbits of non-autonomous maps and their approximation”, JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, vol. 12, 2006, pp. 1103-1126.
Hüls, T.: Homoclinic orbits of non-autonomous maps and their approximation. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS. 12, 1103-1126 (2006).
Hüls, Thorsten. “Homoclinic orbits of non-autonomous maps and their approximation”. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS 12.11 (2006): 1103-1126.

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