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References
Alekseev, V.M., Tikhomirov, V.M., Fomin, S.V.: Optimal control. New York: Consultants Bureau 1987
Arnold, V.I.: First steps in symplectic topology. Russ. Math. Surv.41, 1–21 (1986)
Bialy, M.L., Polterovich, L.V.: Lagrangian singularities of invariant tori of Hamiltonian systems with two degrees of freedom. Invent. Math.97, 291–303 (1989)
Bialy, M.L.: Aubry-Mather sets and Birkhoff's theorem for geodesic flows on the two-dimensional torus. Commun. Math. Phys.126, 13–24 (1989)
Bialy, M.L.: On the number of caustics for invariant tori of Hamiltonian systems with two degrees of freedom. Ergodic Theory Dyn. Syst.11, 273–278 (1991)
Birkhoff, G.D.: Surface transformations and their dynamical application. In: Widder, D.V., et al. (eds.) Collected Math. Papers, vol. 2, pp. 111–229. New York: Dover 1968
Fathi, A.: Une interprétation plus topologique de la démonstration du théorème de Birkhoff. Appendix for Chap. I of Asterisque103–104 (1983)
Gole, C.: Ghost tori for monotone maps. Preprint University of Minnesota
Herman, M.R.: Sur les courbes invariantes par les difféomorphismes de l'anneau. Asterisque103–104 (1983)
Herman, M.R.: Inégalités «a priori» pour des tores Lagrangiens invariants par des difféomorphismes symplectiques. Publ. Math., Inst. Hautes Étud. Sci.70, 47–101 (1989)
Lalonde, F., Sikorav, J.-C.: Sous-variétés lagrangiennes des fibrés cotangents. Comment. Math. Helv.66, 18–33 (1991)
Mather, J.: Non-existence of invariant curves. Ergod. Theory Dyn. Syst.4, 301–309 (1984)
MacKay, R.: A criterion for non-existence of invariant tori for Hamiltonian systems. Physica D36, 64–82 (1989)
MacKay, R., Meiss, J., Stark, J.: Converse KAM-theory for symplectic twist maps. Nonlinearity2, 555–570 (1989)
Moser, J.: Monotone twist mappings and the calculus of variations. Ergod. Theory Dyn. Syst.6, 401–413 (1986)
Polterovich, L.: The Maslov class of Lagrange surfaces and Gromov's pseudoholomorphic curves. Trans. Am. Math. Soc.325, 241–248 (1991)
Polterovich, L.: The second Birkhoff's theorem for optical Hamiltonian systems. Proc. Am. Math. Soc.113, 513–516 (1991)
Polterovich, L.: Monotone Lagrange submanifolds of linear spaces and the Maslov class in cotangent bundles. Math. Z.207, 217–222 (1991)
Sikorav, J.-C.: Formes différentielles fermées non singulières sur len-tore. Comment. Math. Helv.57, 79–106 (1982)
Sullivan, D.: Cycles for the dynamical study of foliated manifolds and complex manifolds. Invent. Math.36, 225–255 (1976)
Viterbo, C.: A new obstruction to embedding Lagrangian tori. Invent. Math.100, 301–320 (1990)