Heteroclinic solutions for perturbed second order systems

Massimiliano Berti

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1997)

  • Volume: 8, Issue: 4, page 251-262
  • ISSN: 1120-6330

Abstract

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The existence of infinitely many heteroclinic orbits implying a chaotic dynamics is proved for a class of perturbed second order Lagrangian systems possessing at least 2 hyperbolic equilibria.

How to cite

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Berti, Massimiliano. "Heteroclinic solutions for perturbed second order systems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.4 (1997): 251-262. <http://eudml.org/doc/244247>.

@article{Berti1997,
abstract = {The existence of infinitely many heteroclinic orbits implying a chaotic dynamics is proved for a class of perturbed second order Lagrangian systems possessing at least 2 hyperbolic equilibria.},
author = {Berti, Massimiliano},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Heteroclinic orbits; Homoclinic orbits; Chaotic dynamics; heteroclinic orbits; perturbed Lagrangian systems; hyperbolic equilibria; Bernoulli shift},
language = {eng},
month = {12},
number = {4},
pages = {251-262},
publisher = {Accademia Nazionale dei Lincei},
title = {Heteroclinic solutions for perturbed second order systems},
url = {http://eudml.org/doc/244247},
volume = {8},
year = {1997},
}

TY - JOUR
AU - Berti, Massimiliano
TI - Heteroclinic solutions for perturbed second order systems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/12//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 4
SP - 251
EP - 262
AB - The existence of infinitely many heteroclinic orbits implying a chaotic dynamics is proved for a class of perturbed second order Lagrangian systems possessing at least 2 hyperbolic equilibria.
LA - eng
KW - Heteroclinic orbits; Homoclinic orbits; Chaotic dynamics; heteroclinic orbits; perturbed Lagrangian systems; hyperbolic equilibria; Bernoulli shift
UR - http://eudml.org/doc/244247
ER -

References

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  1. AMBROSETTI, A. - BADIALE, M., Homoclinics: Poincaré-Melnikov type results via a variational approach. C. R. Acad. Sci. Paris, t. 323, Série I, 1996, 753-758; and Annales I.H.P., to appear. Zbl0887.34042MR1416171DOI10.1016/S0294-1449(97)89300-6
  2. BERTI, M. - BOLLE, P., Homoclinics and Chaotic Behaviour for Perturbed Second Order Systems. Preprint S.N.S. n. 3. Zbl0957.37019MR1746547DOI10.1007/BF02506001
  3. MELNIKOV, V. K., On the stability of the center for time periodic perturbations. Trans. Moscow Math. Soc., 12, 1963, 3-52. Zbl0135.31001MR156048
  4. POINCARÉ, H., Les méthodes nouvelles de la mécanique céleste. Gauthiers-Villars, Paris1889. JFM30.0834.08
  5. SÉRÉ, E., Existence of infinitely many homoclinic orbits in Hamiltonian systems. Math. Zeitschrift, 209, 1992, 27-42. Zbl0725.58017MR1143210DOI10.1007/BF02570817
  6. SÉRÉ, E., Looking for the Bernoulli shift. Ann. Inst. H. Poincaré, Anal. Nonlin., 10, 1993, 561- 590. Zbl0803.58013MR1249107

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