On the existence of transversal heteroclinic orbits in discretized dynamical systems

Zou Y, Beyn W-J (2004)
Nonlinearity 17(6): 2275-2292.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
In this paper we prove the existence of transversal heteroclinic orbits for maps that are obtained from one-step methods applied to a continuous dynamical system. It is assumed that the continuous system exhibits a heteroclinic orbit at a specific value of a parameter. While it is known that analytic vector fields lead to exponentially small splittings of separatrices in the discrete system, we analyse here the case of a continuous system that is smooth of finite order only. Assuming that a certain derivative has a jump discontinuity at a specific hyperplane we show that discretized systems have transversal heteroclinic orbits. The essential step in deriving such a result is a refinement of a previously developed error analysis that applies exponential dichotomy and Fredholm techniques to the discretized system.
Erscheinungsjahr
Zeitschriftentitel
Nonlinearity
Band
17
Ausgabe
6
Seite(n)
2275-2292
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PUB-ID

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Zou Y, Beyn W-J. On the existence of transversal heteroclinic orbits in discretized dynamical systems. Nonlinearity. 2004;17(6):2275-2292.
Zou, Y., & Beyn, W. - J. (2004). On the existence of transversal heteroclinic orbits in discretized dynamical systems. Nonlinearity, 17(6), 2275-2292. doi:10.1088/0951-7715/17/6/014
Zou, Y., and Beyn, W. - J. (2004). On the existence of transversal heteroclinic orbits in discretized dynamical systems. Nonlinearity 17, 2275-2292.
Zou, Y., & Beyn, W.-J., 2004. On the existence of transversal heteroclinic orbits in discretized dynamical systems. Nonlinearity, 17(6), p 2275-2292.
Y. Zou and W.-J. Beyn, “On the existence of transversal heteroclinic orbits in discretized dynamical systems”, Nonlinearity, vol. 17, 2004, pp. 2275-2292.
Zou, Y., Beyn, W.-J.: On the existence of transversal heteroclinic orbits in discretized dynamical systems. Nonlinearity. 17, 2275-2292 (2004).
Zou, Yongkui, and Beyn, Wolf-Jürgen. “On the existence of transversal heteroclinic orbits in discretized dynamical systems”. Nonlinearity 17.6 (2004): 2275-2292.