Blue sky catastrophes in weakly coupled chains of reversible oscillators

Michal Fečkan

doi:10.3934/dcdsb.2003.3.193

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2003, Volume 3, Issue 2: 193-200. Doi: 10.3934/dcdsb.2003.3.193

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Blue sky catastrophes in weakly coupled chains of reversible oscillators

Michal Fečkan^1,

1.
Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava

Received: July 2002

Revised: January 2003

Published: May 2003

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Abstract

Countable many weakly coupled reversible oscillators are investigated. Homoclinic structures are assumed for the anti-integrable limit equations. The existence of infinitely many homoclinic solutions is shown for the chains of perturbed oscillators and each of the homoclinic solutions is accumulated by continuum many breathers with periods tending to infinity. A similar result is shown for the case when heteroclinic loop structures are assumed for the anti-integrable limit equations. Applications are given to several models.

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Mathematics Subject Classification: Primary: 34C37, 34G20, 37C29.

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