A global condition for periodic Duffing-like equations

Montecchiari, Piero; Nolasco, Margherita; Terracini, Susanna

doi:10.1090/S0002-9947-99-02249-7

A global condition for periodic Duffing-like equations
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by Piero Montecchiari, Margherita Nolasco and Susanna Terracini PDF

Trans. Amer. Math. Soc. 351 (1999), 3713-3724 Request permission

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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