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Variational construction of orbits of twist diffeomorphisms
Author(s):
John N.
Mather
Journal:
J. Amer. Math. Soc.
4
(1991),
207-263.
MSC:
Primary 58F13;
Secondary 58F08
MathSciNet review:
1080112
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References:
-
- [1]
- S. Aubry and P. Y. Le Daeron, The discrete Frenkel-Kontorova model and the devil's staircase, Phys. D 7 (1983), 240-258. MR 719055 (85d:58046)
- [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 1 (1988), 1-54. MR 945963 (90a:58145)
- [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 courbes invariantes par les difféomorphismes de l'anneau, vol. 1, Astérisque, nos. 103-104, Soc. Math. France, Paris, 1983. MR 0499079 (58:17041)
- [8]
- -, Inequalités a priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques, preprint, September 1989.
- [9]
- P. Le Calvez, Propriétés générales des applications déviant la verticale, Bull. Soc. Math. France 117 (1989), 69-102. MR 1021564 (90m:58110)
- [10]
- -, Propriétés des attracteurs de Birkhoff, Ergodic Theory Dynamical Systems 8 (1988), 241-310. MR 951271 (90a:58103)
- [11]
- R. S. MacKay, J. D. Meiss, and I. C. Percival, Transport in Hamiltonian systems, Phys. D 13 (1984), 55-81. MR 775278 (86m:58057)
- [12]
- J. N. Mather, Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology 21 (1982), 457-467. MR 670747 (84g:58084)
- [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]
- -, More Denjoy minimal sets for area preserving diffeomorphisms, Comment. Math. Helv. 60 (1985), 508-557. MR 826870 (87f:58086)
- [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]
- -, Destruction of invariant circles, Ergodic Theory Dynamical Systems 8 (1988), 199-214. MR 967638 (89k:58097)
- [18]
- -, Minimal measures, Comment. Math. Helv. 64 (1989), 375-394. MR 998855 (90f:58067)
- [19]
- I. C. Percival, Variational principles for invariant tori and cantori, Sympos. on Nonlinear Dynamcis and Beam-Beam Interactions (M. Month and J. C. Herrara, eds.), American Inst. of Phys. Conf. Proc., no. 57, 1980, pp. 302-310. MR 624989 (82m:58040)
- [20]
- -, A variational principle for invariant tori of fixed frequency, J. Phys. A 12 (1979), L57-L60. MR 524167 (80c:70021)
- [21]
- -, Definite paths and upper bounds on regular regions of velocity phase space, Phys. D 6 (1982/83), 249-259. MR 698194 (84i:58048)
- [22]
- E. C. Titchmarsh, The theory of functions, Clarendon Press, Oxford, 1932.
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Additional Information:
DOI:
10.1090/S0894-0347-1991-1080112-5
PII:
S0894-0347-1991-1080112-5
Copyright of article:
Copyright
1991,
American Mathematical Society
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