A variational approach to chaotic dynamics in periodically forced nonlinear oscillators

  • Elena Bosetto

    Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
  • Enrico Serra

    Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

Abstract

We prove that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics. The approach is based on the construction of multibump type heteroclinic solutions to periodic orbits by the use of global variational methods.

Résumé

On prouve qu’une classe de problèmes contenant l’équation du pendule forcé périodiquement possède les principales caractéristiques de la dynamique chaotique. Les techniques sont basées sur la construction d’orbites hétéroclines de type multibump asymptotiques à des solutions périodiques. Les methodes sont variationnelles globales.

Cite this article

Elena Bosetto, Enrico Serra, A variational approach to chaotic dynamics in periodically forced nonlinear oscillators. Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000), no. 6, pp. 673–709

DOI 10.1016/S0294-1449(00)00054-8