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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 $$\varepsilon x'=f(x) + \varepsilon h(x), \ x(+i) - x(i-) = \varepsilon g(x(i-)), \quad x \in \bbfR^m, \ i \in \bbfZ,$$ 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)].

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