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Blue sky catastrophes in weakly coupled chains of reversible oscillators

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

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