We follow a functional analytic approach to study the problem of chaotic behaviour in time-perturbed discontinuous systems whose unperturbed part has a piecewise C^1 homoclinic solution that crosses transversally the discontinuity manifold. We show that if a certain Melnikov function has a simple zero at some point, then the system has solutions that behave chaotically. Application of this result to quasi periodic systems are also given.
On the chaotic behaviour of discontinuous systems / Battelli, Flaviano; Feckan, M.. - In: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. - ISSN 1040-7294. - STAMPA. - 23:3(2011), pp. 495-540. [10.1007/s10884-010-9197-7]
On the chaotic behaviour of discontinuous systems
BATTELLI, Flaviano;
2011-01-01
Abstract
We follow a functional analytic approach to study the problem of chaotic behaviour in time-perturbed discontinuous systems whose unperturbed part has a piecewise C^1 homoclinic solution that crosses transversally the discontinuity manifold. We show that if a certain Melnikov function has a simple zero at some point, then the system has solutions that behave chaotically. Application of this result to quasi periodic systems are also given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
