Chaotic behavior of rapidly oscillating Lagrangian systems

Francesca Alessio; Vittorio Coti Zelati; Piero Montecchiari

doi:10.3934/dcds.2004.10.687

Article Contents

2004, Volume 10, Issue 3: 687-707. Doi: 10.3934/dcds.2004.10.687

This issue Previous Article Nonplanar and noncollision periodic solutions for $N$-body problems Next Article Stability of solitary waves for a nonlinearly dispersive equation

Chaotic behavior of rapidly oscillating Lagrangian systems

1.
Dipartimento di Matematica, Università di Torino
2.
Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università di Napoli
3.
Dipartimento di Scienze Matematiche, Università Politecnica delle Marche

Received: November 30, 2002

Revised: April 30, 2003

Published: June 2004

Abstract Related Papers Cited by

Abstract

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.

Keywords:

Homoclinic solutions,
chaotic behavior,
almost-periodic and quasiperiodic forcing.

Mathematics Subject Classification: 37J45, 37C29, 34C37, 70K44.

Citation:

Article Metrics

HTML views() PDF downloads(130) Cited by(0)

Chaotic behavior of rapidly oscillating Lagrangian systems

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Chaotic behavior of rapidly oscillating Lagrangian systems

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content