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Nonplanar and noncollision periodic solutions for $N$-body problems
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 |
$ \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.
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