Periodic solutions of the Hamilton-Jacobi equation with a periodic non-homogeneous term and Aubry-Mather theory

Sbornik Mathematics

Volumn 190, Issue 9-10, 1999, Pages 1487-1504

  Sobolevskii A N ^a  

^a NONE

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EID: 0033236641     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/sm1999v190n10abeh000435     Document Type: Article

References (13)

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3. S. Aubry and P. Y. Le Daeron, "The discrete Frenkel-Kontorova model and its extensions. I. Exact results for the ground states", Phys. D 8 (1983), 381-422.
4. J. N. Mather, "Existence of quasiperiodic orbits for twist homeomorphisms of the annulus", Topology 21 (1982), 457-467.
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6. A. N. Sobolevskiǐ, 'On periodic solutions of the Hamilton-Jacobi equation with a periodic forcing term", Uspekhi Mat. Nauk 53:6 (1998), 265-266; English transl. in Russian Math. Surveys 53:6 (1998).
7. H. R. Jauslin, H. O. Kreiss, and J. Moser, "On the forced Burgers equation with periodic boundary conditions", Preprint 1997.
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9. L. Cesari, Optimization: theory and applications. Problems with ordinary differential equations, Appl. Math. vol. 17, Springer-Verlag, Berlin 1983.
10. P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics 69, Pitman, London 1982.
11. J. N. Mather and G. Forni, "Action minimizing orbits in Hamiltonian systems", in Transition to chaos in classical and quantum mechanics, Lecture Notes in Math., no. 1589, Springer-Verlag, Berlin 1994, pp. 92-186.
12. G. D. Birkhoff, "Quelques théorèmes sur les mouvements des systèmes dynamiques", Bull. Soc. Math. France 40 (1912), 305-323;= Collected mathematical papers, Vol. 1, Dover Publications Inc., New York 1968, pp. 654-672.
13. G. D. Birkhoff, "Quelques théorèmes sur les mouvements des systèmes dynamiques", Bull. Soc. Math. France 40 (1912), 305-323;= Collected mathematical papers, Vol. 1, Dover Publications Inc., New York 1968, pp. 654-672.