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On closed orbits for twisted autonomous Tonelli Lagrangian flows. (English) Zbl 1368.53054

In [Calc. Var. Partial Differ. Equ. 27, No. 3, 321–395 (2006; Zbl 1105.37037)], G. Contreras formulated a very general theorem about the existence of periodic motions for autonomous Lagrangian systems over compact configuration spaces. The aim of these lecture notes is to present a generalization of such a theorem to systems which admit only a local Lagrangian description. Among these systems the important example of magnetic flow on surfaces is detailed.

MSC:

53D12 Lagrangian submanifolds; Maslov index
37J50 Action-minimizing orbits and measures (MSC2010)
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70H03 Lagrange’s equations

Citations:

Zbl 1105.37037
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