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- W2069761000 abstract "We consider an autonomous Lagrangian system on a compact manifold M with the Lagrangian L strictly convex in velocity. Let N⊂TM be a hyperbolic invariant torus which is a Peierls set in the sense of the Aubry-Mather theory. This is equivalent to the existence of a calibration of the Lagrangian such that N is the minimum set for L. We prove that N has an infinite number of homoclinic orbits. For any family of homoclinic orbits the first and last intersection points with the boundary of a tubular neighbourhood U of N define sets in U. If there is a component of the set of minimal homoclinics defining contractible sets in U, we obtain an infinite number of multibump homoclinic, periodic and chaotic orbits with given energy. The proof is based on a combination of variational methods of Mather and a generalization of Shilnikov's lemma." @default.
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- W2069761000 date "2001-07-30" @default.
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- W2069761000 title "Symbolic dynamics near minimal hyperbolic invariant tori of Lagrangian systems" @default.
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