In the paper we prove that the Lagrangian system $$\ddot{q} = \alpha(\omega t) V'(q), \quad t \in \R, \ q \in \R^{N},$$ has, for some classes of functions $\alpha$, a chaotic behavior. More precisely the system has multi-bump solutions for all $\omega$ large. These classes of functions include some quasi-periodic and some limit-periodic ones, but not any periodic function. We prove the result using global variational methods.
Chaotic behaviour of rapidly oscillating Lagrangian systems / Alessio, FRANCESCA GEMMA; V., COTI ZELATI; Montecchiari, Piero. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 10:3(2004), pp. 687-707. [10.3934/dcds.2004.10.687]
Chaotic behaviour of rapidly oscillating Lagrangian systems
ALESSIO, FRANCESCA GEMMA;MONTECCHIARI, Piero
2004-01-01
Abstract
In the paper we prove that the Lagrangian system $$\ddot{q} = \alpha(\omega t) V'(q), \quad t \in \R, \ q \in \R^{N},$$ has, for some classes of functions $\alpha$, a chaotic behavior. More precisely the system has multi-bump solutions for all $\omega$ large. These classes of functions include some quasi-periodic and some limit-periodic ones, but not any periodic function. We prove the result using global variational methods.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
