Variational construction of orbits of twist diffeomorphisms
HTML articles powered by AMS MathViewer
- by John N. Mather
- J. Amer. Math. Soc. 4 (1991), 207-263
- DOI: https://doi.org/10.1090/S0894-0347-1991-1080112-5
- PDF | Request permission
References
- 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, DOI 10.1016/0167-2789(83)90129-X S. Aubry, P. Y. Le Daeron, and G. André, Classical ground states of a one-dimensional model for incommensurate structures, preprint, 1982.
- 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 G. D. Birkhoff, Collected mathematical papers, vol. II, Amer. Math. Soc., Providence, RI, 1950. C. Carathéodory, Variationsrechnung und partielle Differentialgleichung erster Ordnung, Teubner, Leipzig, Berlin, 1935. A. Fathi, Appendix to Chapter I of [7].
- M. R. Herman, Sur les mesures invariantes, International Conference on Dynamical Systems in Mathematical Physics (Rennes, 1975) Astérisque, No. 40, Soc. Math. France, Paris, 1976, pp. 103–104 (French). MR 0499079 —, Inequalités a priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques, preprint, September 1989.
- 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
- P. Le Calvez, Propriétés des attracteurs de Birkhoff, Ergodic Theory Dynam. Systems 8 (1988), no. 2, 241–310 (French, with English summary). MR 951271, DOI 10.1017/S0143385700004442
- 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, DOI 10.1016/0167-2789(84)90270-7
- John N. Mather, Existence of quasiperiodic orbits for twist homeomorphisms of the annulus, Topology 21 (1982), no. 4, 457–467. MR 670747, DOI 10.1016/0040-9383(82)90023-4 —, A criterion for the non-existence of invariant circles, Inst. Hautes Études Sci. Publ. Math. 63 (1986), 153-204. —, Letter to R. MacKay, Feb. 21, 1984.
- John N. Mather, More Denjoy minimal sets for area preserving diffeomorphisms, Comment. Math. Helv. 60 (1985), no. 4, 508–557. MR 826870, DOI 10.1007/BF02567431 —, 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.
- John N. Mather, Destruction of invariant circles, Ergodic Theory Dynam. Systems 8$^*$ (1988), no. Charles Conley Memorial Issue, 199–214. MR 967638, DOI 10.1017/S0143385700009421
- John N. Mather, Minimal measures, Comment. Math. Helv. 64 (1989), no. 3, 375–394. MR 998855, DOI 10.1007/BF02564683
- 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
- I. C. Percival, A variational principle for invariant tori of fixed frequency, J. Phys. A 12 (1979), no. 3, L57–L60. MR 524167
- 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, DOI 10.1016/0167-2789(83)90010-6 E. C. Titchmarsh, The theory of functions, Clarendon Press, Oxford, 1932.
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: J. Amer. Math. Soc. 4 (1991), 207-263
- MSC: Primary 58F13; Secondary 58F08
- DOI: https://doi.org/10.1090/S0894-0347-1991-1080112-5
- MathSciNet review: 1080112