Finsler metrics and action potentials. (English) Zbl 0947.37032
Summary: We study the behavior of Mañé’s action potential \(\Phi_k\) associated to a convex superlinear Lagrangian, for \(k\) bigger than the critical value \(c(L)\). We obtain growth estimates for the action potential as a function of \(k\). We also prove that the action potential can be written as \(\Phi_k(x,y)=D_F(x,y)+f(y)-f(x)\) where \(f\) is a smooth function and \(D_F\) is the distance function associated to a Finsler metric.
MSC:
| 37J50 | Action-minimizing orbits and measures (MSC2010) |
| 70H30 | Other variational principles in mechanics |
References:
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