The numerical computation of homoclinic orbits for maps

Beyn W-J, Kleinkauf JM (1997)
SIAM Journal on Numerical Analysis 34(3): 1207-1236.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Transversal homoclinic orbits of maps are known to generate shift dynamics on a set with Canter-like structure. In this paper a numerical method is developed for computation of the corresponding homoclinic orbits. They are approximated by finite-orbit segments subject to asymptotic boundary conditions. We provide a detailed error analysis including a shadowing-type result by which one can infer the existence of a transversal homoclinic orbit from a finite segment. This approach is applied to several examples. In some of them parameters appear and closed loops of homoclinic orbits are found by a path-following algorithm.
Erscheinungsjahr
Zeitschriftentitel
SIAM Journal on Numerical Analysis
Band
34
Ausgabe
3
Seite(n)
1207-1236
ISSN
PUB-ID

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Beyn W-J, Kleinkauf JM. The numerical computation of homoclinic orbits for maps. SIAM Journal on Numerical Analysis. 1997;34(3):1207-1236.
Beyn, W. - J., & Kleinkauf, J. M. (1997). The numerical computation of homoclinic orbits for maps. SIAM Journal on Numerical Analysis, 34(3), 1207-1236. doi:10.1137/S0036142995281693
Beyn, W. - J., and Kleinkauf, J. M. (1997). The numerical computation of homoclinic orbits for maps. SIAM Journal on Numerical Analysis 34, 1207-1236.
Beyn, W.-J., & Kleinkauf, J.M., 1997. The numerical computation of homoclinic orbits for maps. SIAM Journal on Numerical Analysis, 34(3), p 1207-1236.
W.-J. Beyn and J.M. Kleinkauf, “The numerical computation of homoclinic orbits for maps”, SIAM Journal on Numerical Analysis, vol. 34, 1997, pp. 1207-1236.
Beyn, W.-J., Kleinkauf, J.M.: The numerical computation of homoclinic orbits for maps. SIAM Journal on Numerical Analysis. 34, 1207-1236 (1997).
Beyn, Wolf-Jürgen, and Kleinkauf, J. M. “The numerical computation of homoclinic orbits for maps”. SIAM Journal on Numerical Analysis 34.3 (1997): 1207-1236.