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Adiabatic limits of closed orbits for some Newtonian systems in R-n

TitleAdiabatic limits of closed orbits for some Newtonian systems in R-n
Publication TypeJournal Article
Year of Publication2001
AuthorsMalchiodi, A
JournalAsymptotic Anal., 2001, 25, 149-181
Abstract

We deal with a Newtonian system like x\\\'\\\' + V\\\'(x) = 0. We suppose that V: \\\\R^n \\\\to \\\\R possesses an (n-1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarity slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M.

URLhttp://hdl.handle.net/1963/1511

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