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

Fathi, Albert

C. R. Acad. Sci., Paris, Sér. I 324, No. 9, 1043-1046 (1997).

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

Keywords:

KAM theory; Mather theory; Lagrangian systems