The problem is studied of the motion of a particle on a non-flat billiard. The particle is subject to gravity and to a small amplitude periodic forcing and is reflected with respect to the normal axis when hits the boundary of the billiard. We prove that the unperturbed problem has an impact homoclinic orbit and give a Melnikov type condition so that the perturbed problem exhibit chaotic behavior in the sense of Smale’s horseshoe.
On the Chaotic Behavior of non-flat Billiards / Battelli, Flaviano; Michal, Feckan. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - STAMPA. - 19:5(2014), pp. 1442-1464. [10.1016/j.cnsns.2013.04.013]
On the Chaotic Behavior of non-flat Billiards
BATTELLI, Flaviano;
2014-01-01
Abstract
The problem is studied of the motion of a particle on a non-flat billiard. The particle is subject to gravity and to a small amplitude periodic forcing and is reflected with respect to the normal axis when hits the boundary of the billiard. We prove that the unperturbed problem has an impact homoclinic orbit and give a Melnikov type condition so that the perturbed problem exhibit chaotic behavior in the sense of Smale’s horseshoe.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
