Variational construction of connecting orbits
Annales de l'Institut Fourier, Tome 43 (1993) no. 5, pp. 1349-1386.
@article{AIF_1993__43_5_1349_0,
     author = {Mather, John N.},
     title = {Variational construction of connecting orbits},
     journal = {Annales de l'Institut Fourier},
     pages = {1349--1386},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {5},
     year = {1993},
     doi = {10.5802/aif.1377},
     mrnumber = {95c:58075},
     zbl = {0803.58019},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.1377/}
}
TY  - JOUR
AU  - Mather, John N.
TI  - Variational construction of connecting orbits
JO  - Annales de l'Institut Fourier
PY  - 1993
SP  - 1349
EP  - 1386
VL  - 43
IS  - 5
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.1377/
DO  - 10.5802/aif.1377
LA  - en
ID  - AIF_1993__43_5_1349_0
ER  - 
%0 Journal Article
%A Mather, John N.
%T Variational construction of connecting orbits
%J Annales de l'Institut Fourier
%D 1993
%P 1349-1386
%V 43
%N 5
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.1377/
%R 10.5802/aif.1377
%G en
%F AIF_1993__43_5_1349_0
Mather, John N. Variational construction of connecting orbits. Annales de l'Institut Fourier, Tome 43 (1993) no. 5, pp. 1349-1386. doi : 10.5802/aif.1377. http://archive.numdam.org/articles/10.5802/aif.1377/

[Arn1] V.I. Arnold, First steps in symplectic topology, Russ. Math. Surv., 41 (1986), 1-21. | MR | Zbl

[Arn2] V.I. Arnold, Instability of dynamical systems with many degrees of freedom, Dokl. Akad. Nauk SSSR, 156 (1964), 9-12. | MR | Zbl

[A-LD-A] S. Aubry, P.Y. Ledaeron, G. André, Classical ground-states of a one dimensional model for incommensurate structures, preprint (1982).

[Aub] S. Aubry, The Devil's Staircase Transformation in Incommensurate Lattices in the Riemann Problem, Complete Integrability, and Arithmetic Applications, ed. by Chudnovsky and Chudnovsky, Lecture Notes in Math., Springer-Verlag, 925 (1982), 221-245.

[Bal] J. Ball, V. Mizel, One dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation, Arch. Ration. Mech. Anal., 90 (1985), 325-388. | MR | Zbl

[Ban1] V. Bangert, Mather sets for twist maps and geodesics on tori, Dyn. Rep., 1 (1988), 1-56. | MR | Zbl

[Ban2] V. Bangert, Minimal geodesics, Ergod. Th. & Dynam. Sys., 10 (1989), 263-286. | MR | Zbl

[Ban3] V. Bangert, Geodesic Rays, Busemann Functions, and Monotone Twist Maps, Calc. Var. 2 (1994), 49-63. | Zbl

[B-K] D. Bernstein, A. Katok, Birkhoff periodic orbits for small perturbations of completely integrable systems with convex Hamiltonians, Invent. Math., 88 (1987), 225-241. | EuDML | MR | Zbl

[B-P] M. Bialy and L. Polterovich, Hamiltonian systems, Lagrangian tori, and Birkhoff's theorem, Math. Ann., 292 (1992), 619-627. | Zbl

[Bol] S. Bolotin, Homoclinic orbits to invariant tori of symplectic diffeomorphisms and Hamiltonian systems, Advances in Soviet Math., to appear. | Zbl

[Cara] C. Caratheodory, Variationsrechnung und partielle Differentialgleichung erster Ordnung, B. G. Teubner, Leipzig, Berlin, 1935. | JFM | Zbl

[Cart] E. Cartan, Leçons sur les invariants intégraux, Herman, Paris, 1922.

[Den] J. Denzler, Mather sets for plane Hamiltonian systems, J. Appl. Math. Phys. (ZAMP), 38 (1987), 791-812. | MR | Zbl

[Her1] M. Herman, Sur la conjugaison différentiable des difféomorphismes du circle à des rotations, IHES Publ. Math., 49 (1979), 5-234. | Numdam | MR | Zbl

[Her2] M. Herman, Existence et non existence de tores invariantes par des difféomorphismes symplectiques, preprint (1988). | Numdam | Zbl

[Kat] A. Katok, Minimal orbits for small parturbations of completely integrable Hamiltonian systems, preprint (1988). | Zbl

[K-B] N. Kryloff, N. Bogoliuboff, La theorie générale de la mesure et son application à l'étude des systèmes dynamiques de la mécanique non linéaire, Ann. Math., II Ser, 38 (1937), 65-113. | JFM | Zbl

[Ma샱1] R. Ma샑É, Global Variational Methods in Conservative Dynamics, 18° Coloquio Brasileiro de Mathemática, IMPA, 1991.

[Ma샱2] R. Ma샑É, On the minimizing measures of Lagrangian Dynamical Systems, Nonlinearity, 5 (1992), 623-638. | MR | Zbl

[Ma샱3] R. Ma샑É, Generic Properties and Problems of Minimizing Measures of Lagrangian Systems, preprint.

[Ma1] J. Mather, More Denjoy minimal sets for area preserving diffeomorphisms, Comment. Math. Helv., 60 (1985), 508-557. | MR | Zbl

[Ma2] J. Mather, Modulus of Continuity for Peierls's Barrier, Periodic Solutions of Hamiltonian Systems and Related Topics, ed. by Rabinowitz, et. al., NATO ASI, Series C : vol. 209, Dordrecht : D. Reidel (1987), 177-202. | MR | Zbl

[Ma3] J. Mather, Destruction of Invariant Circles, Ergodic Theory and Dynamical Systems, 8* (vol. dedicated to Charles Conley) (1988), 199-214. | MR | Zbl

[Ma4] J. Mather, Minimal Measures, Comm. Math. Helv., 64 (1989), 375-394. | MR | Zbl

[Ma5] J. Mather, Variational Construction of Orbits of Twist Diffeomorphisms, Journal of the American Math. Soc., 4 (1991), 207-263. | MR | Zbl

[Ma6] J. Mather, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z., 207 (1991), 169-207. | MR | Zbl

[Ma7] J. Mather, Differentiability of the minimal average action as a function of the rotation number, Bol. Soc. Bras. Mat., 21 (1990), 59-70. | MR | Zbl

[Mo] J. Moser, Monotone Twist Mappings and the Calculus of Variations, Ergodic Theory and Dyn. Syst., 6 (1986), 401-413. | MR | Zbl

[N-S] V. Nemytskii, V. Stepanov, Qualitative Theory of Differential Equations, Princeton Univ. Press, Princeton, N.J., 1960. | MR | Zbl

[Roc] R. Rockafeller, Convex Analysis, Princeton Math. Ser, Princeton, N.J., 28 (1970). | MR | Zbl

[Sch] S. Schwartzman, Asymptotic cycles, Ann. Math., 66 (1957), 270-284. | MR | Zbl

[Yoc] J.-C. Yoccoz, Travaux de Herman sur les Tores invariants, Séminaire Bourbaki, vol. 1991/92, exposé 754, Astérisque, 206 (1992). | Numdam | MR | Zbl

Cité par Sources :