Existence of multiple normal mode trajectories on convex energy surfaces of even, classical Hamiltonian systems

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Abstract

Hamiltonian systems of n degrees of freedom for which the Hamiltonian is a function that is even both in its joint n coordinate variables as well as in its joint n momentum variables are discussed. For such systems the number of distinct trajectories which correspond to particular periodic solutions (normal modes) with the same energy, is investigated. To that end a constrained dual action principle is introduced. Applying min-max methods to this variational problem, several results are obtained, among which the existence of at least n distinct trajectories if specific conditions are satisfied.
Original languageEnglish
Pages (from-to)70-89
JournalJournal of differential equations
Volume57
Issue number1
DOIs
Publication statusPublished - 1985
Externally publishedYes

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