On manifolds of connecting orbits in discretizations of dynamical systems

Zou YK, Beyn W-J (2003)
Nonlinear Analysis: Theory, Methods & Applications 52(5): 1499-1520.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
It is shown that one-step methods, when applied to a one-parametric dynamical system with a homoclinic orbit, exhibit a closed loop of discrete homoclinic orbits. On this loop, the parameter varies periodically while the orbit shifts its index after one revolution. We show that at least two homoclinic tangencies occur on this loop. Our approach works for systems with finite smoothness and also applies to general connecting orbits. It provides an alternative to the interpolation approach by Fiedler and Scheurle (Mem. Amer. Math. Soc. 119 (570) (1996)) and it allows to recover some of their results on exponentially small splittings of separatrices by using some recent backward error analysis for the analytic case. (C) 2002 Elsevier Science Ltd. All rights reserved.
Stichworte
homoclinic; tangencies; connecting orbits; dynamical systems; one-step methods
Erscheinungsjahr
2003
Zeitschriftentitel
Nonlinear Analysis: Theory, Methods & Applications
Band
52
Ausgabe
5
Seite(n)
1499-1520
ISSN
0362-546X
Page URI
https://pub.uni-bielefeld.de/record/1612809

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Zou YK, Beyn W-J. On manifolds of connecting orbits in discretizations of dynamical systems. Nonlinear Analysis: Theory, Methods & Applications. 2003;52(5):1499-1520.
Zou, Y. K., & Beyn, W. - J. (2003). On manifolds of connecting orbits in discretizations of dynamical systems. Nonlinear Analysis: Theory, Methods & Applications, 52(5), 1499-1520. doi:10.1016/S0362-546X(02)00269-9
Zou, Y. K., and Beyn, W. - J. (2003). On manifolds of connecting orbits in discretizations of dynamical systems. Nonlinear Analysis: Theory, Methods & Applications 52, 1499-1520.
Zou, Y.K., & Beyn, W.-J., 2003. On manifolds of connecting orbits in discretizations of dynamical systems. Nonlinear Analysis: Theory, Methods & Applications, 52(5), p 1499-1520.
Y.K. Zou and W.-J. Beyn, “On manifolds of connecting orbits in discretizations of dynamical systems”, Nonlinear Analysis: Theory, Methods & Applications, vol. 52, 2003, pp. 1499-1520.
Zou, Y.K., Beyn, W.-J.: On manifolds of connecting orbits in discretizations of dynamical systems. Nonlinear Analysis: Theory, Methods & Applications. 52, 1499-1520 (2003).
Zou, Y. K., and Beyn, Wolf-Jürgen. “On manifolds of connecting orbits in discretizations of dynamical systems”. Nonlinear Analysis: Theory, Methods & Applications 52.5 (2003): 1499-1520.