Homoclinics and complex dynamics in slowly oscillating systems

Antonio Ambrosetti; Massimiliano Berti

doi:10.3934/dcds.1998.4.393

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1998, Volume 4, Issue 3: 393-403. Doi: 10.3934/dcds.1998.4.393

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Homoclinics and complex dynamics in slowly oscillating systems

Antonio Ambrosetti^1, and
Massimiliano Berti¹

1.
Department of Mathematics, Scuola Normale Superiore, Pisa, 56100

Received: December 31, 1996

Revised: December 31, 1997

Published: June 1998

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Abstract

This paper deals with a class of second order dynamical systems with slowly oscillating coefficients, see $(1)$. Using variational methods, perturbative in nature, we show that $(1)$ has multi-bump homoclinics and a complex dynamics.

Keywords:

Homoclinics and complex dynamics,
oscillating systems.

Mathematics Subject Classification: 58E05, 34C37.

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