| Hyperbolic Dynamics of Euler-Lagrange Flows on Prescribed Energy Levels | |||||||||||||||
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| . The aim of this paper is to describe some recent results concerning the dynamics of Euler-Lagrange flows on prescribed energy levels. We show that if an Anosov energy level has a splitting of class C 1 then it must contain minimizing measures with non-zero homology. 1. Introduction The aim of this paper is to describe some recent results concerning the dynamics of Euler-Lagrange flows on prescribed energy levels. These results have been obtained using variational methods. Throughout this paper the Euler-Lagrange flows the we shall consider are generated by convex and superlinear Lagrangians on closed connected manifolds M . A very interesting aspect of the dynamics of the Euler-Lagrange flows is given by those orbits or invariant measures that satisfy some global variational properties, instead of the local ones that every orbit satisfy. Research on these special orbits goes back to M. Morse [39] and Hedlund [25] and has reappeared in recent years in the work of V. Bangert [2], M.... | |||||||||||||||
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