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Zbl 0919.34016
Battelli, Flaviano; Fečkan, Michal
Chaos in singular impulsive O. D. E.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 28, No.4, 655-671 (1997). ISSN 0362-546X

The authors establish conditions under which the Poincaré map for the periodic impulsive system $$\varepsilon x'=f(x) + \varepsilon h(x), \ x(+i) - x(i-) = \varepsilon g(x(i-)), \quad x \in \bbfR^m, \ i \in \bbfZ,$$ has a transversal homoclinic point for all small $\varepsilon >0$ [see {\it M. Fečkan}, Boll. Unione Mat. Ital., VII. Ser. B 10, No. 1, 175-198 (1996; Zbl 0863.34016)].
[S.I.Trofimchuk (Kiev)]
MSC 2000:
*34A37 Differential equations with impulses
34C28 Other types of "recurrent" solutions of ODE
34E15 Asymptotic singular perturbations, general theory (ODE)
34C37 Homoclinic and heteroclinic solutions of ODE

Keywords: transversal homoclinic orbits; Melnikov functions; Lyapunov-Schmidt procedure

Citations: Zbl 0863.34016

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