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A weak KAM theorem and Mather’s theory of Lagrangian systems. (Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens.) (French) Zbl 0885.58022

The author gives a weak version of the Kolmogorov-Arnold-Moser theorem in the framework of Mather’s theory of Lagrangian systems. A particular case has already been established by J. L. Lions, G. C. Papanicolaou and by S. Varadhan.
Reviewer: Y.Kozai (Tokyo)

MSC:

37J50 Action-minimizing orbits and measures (MSC2010)
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
35F20 Nonlinear first-order PDEs
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