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Conjugate weak KAM solutions and Peierls’s barriers. (Solutions KAM faibles conjuguées et barrières de Peierls.) (French) Zbl 0943.37031

Summary: We continue our study of the weak KAM theorem, which we obtained in our previous note [ibid. 324, 1043-1046 (1997; Zbl 0885.58022)]. We state the connection between this theorem and the Peierls’s barriers as defined by Mather. From this connection one can deduce the fact, due to Mañé, that the dynamics on the set of \(M\)-minimizing extremals is chain transitive.

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology

Citations:

Zbl 0885.58022
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