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Homoclinical structure of the chaotic attractor

In the reference [Akhmet MU. Devaney chaos of a relay system. Commun Nonlinear Sci Numer Simulat 2009:14:1486-93.], a relay system was introduced, which admits a chaotic attractor with Devaney's ingredients. Now, we prove that the attractor consists of homo-clinic solutions. A simulation of the attractor is provided for a pendulum equation. Similar results for impulsive differential equations were announced in the plenary talk [Akhmet MU. Hyperbolic sets of impact systems. Dyn Contin Discrete Impuls Syst Set A Math Anal 2008:15(Suppl. S1):1-2. Proceedings of the 5th international conference on impulsive and hybrid dynamical systems and applications, Beijin: Watan Press: 2008.]. (C) 2009 Elsevier B.V. All rights reserved.