A global condition for periodic Duffing-like equations. (English) Zbl 0926.37005

Montecchiari, Piero; Nolasco, Margherita; Terracini, Susanna

Trans. Am. Math. Soc. 351, No. 9, 3713-3724 (1999).

Summary: The authors study Duffing-like equations of the type \(\ddot q= q - \alpha(t)W'(q) \), ith \(\alpha \in C({\mathbb{R}},{\mathbb{R}})\) periodic. They prove that if the stable and unstable manifolds to the origin do not coincide, then the system exhibits positive topological entropy.

MSC:

37C29	Homoclinic and heteroclinic orbits for dynamical systems
37B40	Topological entropy
34C37	Homoclinic and heteroclinic solutions to ordinary differential equations
37J45	Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)

Keywords:

Duffing equations; homoclinic orbits; multibump solutions; minimax argument

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