# American Institute of Mathematical Sciences

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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