Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 

 

Variational construction of orbits of twist diffeomorphisms


Author: John N. Mather
Journal: J. Amer. Math. Soc. 4 (1991), 207-263
MSC: Primary 58F13; Secondary 58F08
MathSciNet review: 1080112
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] Serge Aubry, The twist map, the extended Frenkel-Kontorova model and the devil’s staircase, Phys. D 7 (1983), no. 1-3, 240–258. Order in chaos (Los Alamos, N.M., 1982). MR 719055, 10.1016/0167-2789(83)90129-X
  • [2] S. Aubry, P. Y. Le Daeron, and G. André, Classical ground states of a one-dimensional model for incommensurate structures, preprint, 1982.
  • [3] V. Bangert, Mather sets for twist maps and geodesics on tori, Dynamics reported, Vol. 1, Dynam. Report. Ser. Dynam. Systems Appl., vol. 1, Wiley, Chichester, 1988, pp. 1–56. MR 945963
  • [4] G. D. Birkhoff, Collected mathematical papers, vol. II, Amer. Math. Soc., Providence, RI, 1950.
  • [5] C. Carathéodory, Variationsrechnung und partielle Differentialgleichung erster Ordnung, Teubner, Leipzig, Berlin, 1935.
  • [6] A. Fathi, Appendix to Chapter I of [7].
  • [7] M. R. Herman, Sur les mesures invariantes, International Conference on Dynamical Systems in Mathematical Physics (Rennes, 1975) Soc. Math. France, Paris, 1976, pp. 103–104. Astérisque, No. 40 (French). MR 0499079
  • [8] -, Inequalités a priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques, preprint, September 1989.
  • [9] Patrice Le Calvez, Propriétés générales des applications déviant la verticale, Bull. Soc. Math. France 117 (1989), no. 1, 69–102 (French, with English summary). MR 1021564
  • [10] P. Le Calvez, Propriétés des attracteurs de Birkhoff, Ergodic Theory Dynam. Systems 8 (1988), no. 2, 241–310 (French, with English summary). MR 951271, 10.1017/S0143385700004442
  • [11] R. S. MacKay, J. D. Meiss, and I. C. Percival, Transport in Hamiltonian systems, Phys. D 13 (1984), no. 1-2, 55–81. MR 775278, 10.1016/0167-2789(84)90270-7
  • [12] John N. Mather, Existence of quasiperiodic orbits for twist homeomorphisms of the annulus, Topology 21 (1982), no. 4, 457–467. MR 670747, 10.1016/0040-9383(82)90023-4
  • [13] -, A criterion for the non-existence of invariant circles, Inst. Hautes Études Sci. Publ. Math. 63 (1986), 153-204.
  • [14] -, Letter to R. MacKay, Feb. 21, 1984.
  • [15] John N. Mather, More Denjoy minimal sets for area preserving diffeomorphisms, Comment. Math. Helv. 60 (1985), no. 4, 508–557. MR 826870, 10.1007/BF02567431
  • [16] -, Modulus of continuity for Peierls's barrier, Periodic Solutions of Hamiltonian Systems and Related Topics (P. H. Rabinowitz et al., eds.), NATO ASI Series C, vol. 209, Reidel, Dordrecht, 1987, pp. 177-202.
  • [17] John N. Mather, Destruction of invariant circles, Ergodic Theory Dynam. Systems 8* (1988), no. Charles Conley Memorial Issue, 199–214. MR 967638, 10.1017/S0143385700009421
  • [18] John N. Mather, Minimal measures, Comment. Math. Helv. 64 (1989), no. 3, 375–394. MR 998855, 10.1007/BF02564683
  • [19] I. C. Percival, Variational principles for invariant tori and cantori, Nonlinear dynamics and the beam-beam interaction (Sympos., Brookhaven Nat. Lab., New York, 1979) AIP Conf. Proc., vol. 57, Amer. Inst. Physics, New York, 1980, pp. 302–310. MR 624989
  • [20] I. C. Percival, A variational principle for invariant tori of fixed frequency, J. Phys. A 12 (1979), no. 3, L57–L60. MR 524167
  • [21] R. P. A. C. Newman and I. C. Percival, Definite paths and upper bounds on regular regions of velocity phase space, Phys. D 6 (1982/83), no. 2, 249–259. MR 698194, 10.1016/0167-2789(83)90010-6
  • [22] E. C. Titchmarsh, The theory of functions, Clarendon Press, Oxford, 1932.

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 58F13, 58F08

Retrieve articles in all journals with MSC: 58F13, 58F08


Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1991-1080112-5
Article copyright: © Copyright 1991 American Mathematical Society