Displaying similar documents to “On the multiplicity of brake orbits and homoclinics in Riemannian manifolds”

A variational construction of chaotic trajectories for a Hamiltonian system on a torus

S. V. Bolotin, P. H. Rabinowitz (1998)

Bollettino dell'Unione Matematica Italiana

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A geometric criterion for the existence of chaotic trajectories of a Hamiltonian system with two degrees of freedom and the configuration space a torus is given. As an application, positive topological entropy is established for a double pendulum problem.

Morse index and bifurcation of -geodesics on semi Riemannian manifolds

Monica Musso, Jacobo Pejsachowicz, Alessandro Portaluri (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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Given a one-parameter family { g λ : λ ∈ [ a , b ] } of semi Riemannian metrics on an -dimensional manifold , a family of time-dependent potentials { V λ : λ ∈ [ a , b ] } and a family { σ λ : λ ∈ [ a , b ] } of trajectories connecting two points of the mechanical system defined by ( g λ , V λ ) , we show that there are trajectories bifurcating from the trivial branch σ λ if the generalized Morse indices μ ( σ a ) and μ ( σ b ) are different. If the data are analytic we obtain estimates for the number of bifurcation points on the branch and, in particular, for the number of strictly...