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Smooth critical sub-solutions of the Hamilton-Jacobi equation. (English) Zbl 1125.37044

Summary: We establish the existence of smooth critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds for smooth convex Hamiltonians, that is in the context of weak KAM theory, under the assumption that the Aubry set is the union of finitely many hyperbolic periodic orbits or fixed points.

MSC:

37J50 Action-minimizing orbits and measures (MSC2010)
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
70H20 Hamilton-Jacobi equations in mechanics
37D05 Dynamical systems with hyperbolic orbits and sets
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