May  2003, 3(2): 193-200. doi: 10.3934/dcdsb.2003.3.193

Blue sky catastrophes in weakly coupled chains of reversible oscillators

1. 

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

Received  July 2002 Revised  January 2003 Published  February 2003

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.
Citation: Michal Fečkan. Blue sky catastrophes in weakly coupled chains of reversible oscillators. Discrete and Continuous Dynamical Systems - B, 2003, 3 (2) : 193-200. doi: 10.3934/dcdsb.2003.3.193
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