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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A global condition for
periodic Duffing-like equations


Authors: Piero Montecchiari, Margherita Nolasco and Susanna Terracini
Journal: Trans. Amer. Math. Soc. 351 (1999), 3713-3724
MSC (1991): Primary 58E05, 70H35, 34C37, 58F15
Published electronically: March 1, 1999
MathSciNet review: 1487629
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Abstract: We study Duffing-like equations of the type $\ddot q= q - \alpha (t)W'(q) $,with $\alpha \in C({\mathbb{R}},{\mathbb{R}})$ periodic. We prove that if the stable and unstable manifolds to the origin do not coincide, then the system exhibits positive topological entropy.


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Additional Information

Piero Montecchiari
Affiliation: Dipartimento di Matematica, Universitá degli studi di Trieste, Piazzale Europa 1, 34013 Trieste, Italy
Email: montec@univ.trieste.it

Margherita Nolasco
Affiliation: S.I.S.S.A., via Beirut 4, 34013 Trieste, Italy
Email: nolasco@neumann.sissa.it

Susanna Terracini
Affiliation: Dipartimento di Matematica del Politecnico, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Email: suster@ipmma1.mate.polimi.it

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02249-7
PII: S 0002-9947(99)02249-7
Keywords: Duffing equations, homoclinic orbits, multibump solutions, minimax argument.
Received by editor(s): July 16, 1996
Received by editor(s) in revised form: March 31, 1997
Published electronically: March 1, 1999
Article copyright: © Copyright 1999 American Mathematical Society