Bernard, Patrick Smooth critical sub-solutions of the Hamilton-Jacobi equation. (English) Zbl 1125.37044 Math. Res. Lett. 14, No. 3, 503-511 (2007). 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. Cited in 11 Documents 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 Keywords:weak KAM theory; Aubry set; hyperbolic periodic orbits; hyperbolic fixed points; minimization of the Lagrangian action PDFBibTeX XMLCite \textit{P. Bernard}, Math. Res. Lett. 14, No. 3, 503--511 (2007; Zbl 1125.37044) Full Text: DOI arXiv