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Chaos in singular impulsive O. D. E. (English) Zbl 0919.34016

The authors establish conditions under which the Poincaré map for the periodic impulsive system

εx ' =f(x)+εh(x),x(+i)-x(i-)=εg(x(i-)),x m ,i,

has a transversal homoclinic point for all small ε>0 [see M. Fečkan, Boll. Unione Mat. Ital., VII. Ser. B 10, No. 1, 175-198 (1996; Zbl 0863.34016)].

MSC:
34A37Differential equations with impulses
34C28Complex behavior, chaotic systems (ODE)
34E15Asymptotic singular perturbations, general theory (ODE)
34C37Homoclinic and heteroclinic solutions of ODE