Fathi, Albert Conjugate weak KAM solutions and Peierls’s barriers. (Solutions KAM faibles conjuguées et barrières de Peierls.) (French) Zbl 0943.37031 C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 6, 649-652 (1997). 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. Cited in 1 ReviewCited in 41 Documents 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 Keywords:weak KAM theorem; Peierls’s barriers; chain transitive dynamics Citations:Zbl 0885.58022 PDFBibTeX XMLCite \textit{A. Fathi}, C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 6, 649--652 (1997; Zbl 0943.37031) Full Text: DOI