Density of chaotic dynamics in periodically forced pendulum-type equations
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 12 (2001) no. 2, pp. 107-113.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We announce that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics for a dense set of forcing terms in a space of periodic functions with zero mean value. The approach is based on global variational methods.
Si annuncia che una classe di problemi contenente l’equazione del pendolo forzato periodicamente presenta le principali caratteristiche della dinamica caotica per un insieme denso di termini forzanti nell’insieme delle funzioni periodiche a media nulla. I metodi sono di natura variazionale.
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Bosetto, Elena; Serra, Enrico; Terracini, Susanna. Density of chaotic dynamics in periodically forced pendulum-type equations. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 12 (2001) no. 2, pp. 107-113. http://geodesic.mathdoc.fr/item/RLIN_2001_9_12_2_a3/

[1] F. Alessio - M. Calanchi - E. Serra, Complex dynamics in a class of reversible equations. Progr. in Diff. Eqs. Appl., 43, Birkhäuser, Boston 2001, 147-159. | MR | Zbl

[2] F. Alessio - P. Caldiroli - P. Montecchiari, Genericity of the multibump dynamics for almost periodic Duffing-like systems. Proc. Royal Soc. Edinburgh, 129A, 1999, 885-901. | DOI | MR | Zbl

[3] A. Ambrosetti - M. Badiale, Homoclinics: Poincaré-Melnikov type results via a variational approach. Ann. IHP, Anal. non Linéaire, 15, 1998, 233-252. | fulltext EuDML | fulltext mini-dml | DOI | MR | Zbl

[4] E. Bosetto - E. Serra, A variational approach to chaotic dynamics in periodically forced nonlinear oscillators. Ann. IHP, Anal. non Linéaire, 17, 2000, 673-709. | fulltext EuDML | fulltext mini-dml | DOI | MR | Zbl

[5] E. Bosetto - E. Serra - S. Terracini, Generic-type results for chaotic dynamics in equations with periodic forcing terms. Preprint 2000. | DOI | MR | Zbl

[6] B. Buffoni - E. Séré, A global condition for quasi-random behavior in a class of conservative systems. Comm. Pure Appl. Math., 49, 1996, 285-305. | DOI | MR | Zbl

[7] M. Calanchi - E. Serra, Homoclinic solutions to periodic motions in a class of reversible equations. Calc. Var. and PDEs, 9, 1999, 157-184. | DOI | MR | Zbl

[8] P. Martinez-Amores - J. Mawhin - R. Ortega - M. Willem, Generic results for the existence of nondegenerate periodic solutions of some differential systems with periodic nonlinearities. J. Diff. Eq., 91, 1991, 138-148. | DOI | MR | Zbl

[9] J. N. Mather, Variational construction of orbits of twist diffeomorphisms. J. of AMS, 4, 1991, 207-263. | DOI | MR | Zbl

[10] P. H. Rabinowitz, Heteroclinics for a reversible Hamiltonian system. Ergod. Th. and Dyn. Sys., 14, 1994, 817-829. | DOI | MR | Zbl

[11] P. H. Rabinowitz, Heteroclinics for a reversible Hamiltonian system, 2. Diff. and Int. Eq., 7, 1994, 1557-1572. | MR | Zbl

[12] P. H. Rabinowitz, Connecting orbits for a reversible Hamiltonian system. Ergod. Th. and Dyn. Sys., to appear. | DOI | MR | Zbl

[13] E. Séré, Looking for the Bernoulli shift. Ann. IHP, Anal. non Linéaire, 10, 1993, 561-590. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[14] E. Serra - M. Tarallo - S. Terracini, On the structure of the solution set of forced pendulum-type equations. J. Diff. Eq., 131, 1996, 189-208. | DOI | MR | Zbl

[15] S. Terracini, Non degeneracy and chaotic motions for a class of almost-periodic Lagrangian systems. Nonlin. Anal. TMA, 37, 1999, 337-361. | DOI | MR | Zbl

[16] S. Wiggins, Introduction to applied nonlinear dynamical systems and chaos. Springer-Verlag, New York 1990. | MR | Zbl