Bibliography. [1] S.B. Angenent, The periodic orbits of an area preserving twist map, Comm. Math. Phys. 115 (1988), no. 3,

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1 Bibliography [1] S.B. Angenent, The periodic orbits of an area preserving twist map, Comm. Math. Phys. 115 (1988), no. 3, [2], Monotone recurrence relations, their Birkhoff orbits and topological entropy, Ergodic Theory Dynam. Systems 10 (1990), [3] V.I. Arnol d, Instability of dynamical systems with many degrees of freedom, Dokl. Akad. Nauk SSSR 156 (1964), [4], Geometrical methods in the theory of ordinary differential equations, second ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 250, Springer-Verlag, New York, [5], Mathematical methods of classical mechanics, Graduate texts in mathematics, no. 60, Springer, New York, [6] S. Aubry, Devil s staircase and order without periodicity in classical condensed matter, J. Physique 44 (1983), no. 2, [7], The twist map, the extended Frenkel-Kontorova model and the devil s staircase, Phys. D 7 (1983), no. 1-3, , Order in chaos (Los Alamos, N.M., 1982). [8] 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), no. 3, [9] S. Aubry, R.S. MacKay, and C. Baesens, Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models, Phys. D 56 (1992), no. 2-3, MR (93e:58144) [10] C. Baesens and R.S. MacKay, Cantori for multiharmonic maps, Phys. D 69 (1993), no. 1-2, [11] V. Bangert, The existence of gaps in minimal foliations, Aequationes Math. 34 (1987), no. 2-3,

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3 Bibliography 181 [28], A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 4, [29], Ground states and critical points for Aubry-Mather theory in statistical mechanics, J. Nonlinear Sci. 20 (2010), no. 2, [30] L.C. Evans, Partial differential equations, American Mathematical Society, [31] A. Fathi, The weak KAM theorem in Lagrangian dynamics, Seventh preliminary edition, Preprint, [32] L.M. Floría and J.J. Mazo, Dissipative dynamics of the Frenkel-Kontorova model, Advances in Physics 45 (1996), no. 6, [33] G. Forni, Analytic destruction of invariant circles, Ergodic Theory Dynam. Systems 14 (1994), no. 2, [34] J. Frenkel and T. Kontorova, On the theory of plastic deformation and twinning, Acad. Sci. U.S.S.R. J. Phys. 1 (1939), MR (1,190b) [35] C. Golé, A new proof of the Aubry-Mather s theorem, Math. Z. 210 (1991), [36], Ghost circles for twist maps, J. Differential Equations 97 (1992), no. 1, [37], Symplectic twist maps, Translations of Mathematical Monographs, World Scientific Publishing Co. Pte. Ltd., [38] G.R. Hall, A topological version of a theorem of Mather on twist maps, Ergodic Theory Dynam. Systems 4 (1984), no. 4, [39] G.A. Hedlund, Geodesics on a two-dimensional Riemannian manifold with periodic coefficients, Ann. of Math. (2) 33 (1932), no. 4, [40] M.W. Hirsch, Differential topology, Springer, [41] A. Katok, Some remarks of Birkhoff and Mather twist map theorems, Ergodic Theory Dynamical Systems 2 (1982), no. 2, (1983). [42] A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, Cambridge University Press, [43] H. Koch, R. de la Llave, and C. Radin, Aubry-Mather theory for functions on lattices, Discr. Cont. Dyn. Syst. 3 (1997), no. 1, [44] A.J. Lichtenberg and M.A. Lieberman, Regular and chaotic dynamics, second ed., Applied Mathematical Sciences, vol. 38, Springer-Verlag, New York, 1992.

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6 184 Bibliography