July  2004, 10(3): 687-707. doi: 10.3934/dcds.2004.10.687

Chaotic behavior of rapidly oscillating Lagrangian systems

1. 

Dipartimento di Matematica, Università di Torino, Italy

2. 

Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università di Napoli, Italy

3. 

Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Italy

Received  December 2002 Revised  May 2003 Published  January 2004

In the paper we prove that the Lagrangian system

$ \ddot{q} = \alpha(\omega t) V'(q), \quad t \in \mathbb R, q \in \mathbb R^N,$ $\qquad\qquad (L_\omega)$

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.

Citation: Francesca Alessio, Vittorio Coti Zelati, Piero Montecchiari. Chaotic behavior of rapidly oscillating Lagrangian systems. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 687-707. doi: 10.3934/dcds.2004.10.687
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