Lagrangian systems on hyperbolic manifolds

Ergodic Theory and Dynamical Systems

Volumn 19, Issue 5, 1999, Pages 1157-1173

  Boyland, Philip ^a   Golé, Christophe ^b  

^a UNIVERSITY OF FLORIDA   (United States)

^b SMITH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033413369     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385799133893     Document Type: Article

References (28)

1. R. Abraham and J. E. Marsden. Foundations of Mechanics. Addison-Wesley, 1985.
2. S. Aubry and P. Y. Le Daeron. The discrete Frenkel-Kontorova model and its extensions. I: Exact results for the ground states. Physica 8D (1983), 381-422.
3. V. Bangert. Mather sets for twist maps and geodesics on tori. Dynamics Reported Vol. 1. Eds. U. Kirchgraber and H. O. Walther. Wiley, Chichester, 1988.
4. V. Bangert. Minimal geodesies. Ergod. Th. & Dynam. Sys. 10 (1989), 263-286.
5. T. Bedford, M. Keane and C. Series (Eds). Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces. Oxford University Press, 1991.
6. V. Benci. Periodic solutions for Lagrangian systems on compact manifolds. J. Diff. Eq. 63 (1986), 135-161.
7. D. Bernstein and A. Katok. Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems. Invent. Math. 88 (1987), 225-241.
8. P. Boyland. New dynamical invariants on hyperbolic manifolds. Israel J. Math. to appear.
9. P. Boyland and C. Golé. Dynamical stability in Lagrangian systems. Proc. NATO Advanced Study Institute on Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, Spain). Kluwer, 1999, pp. 90-114.
10. M. Bialy and L. Polterovitch. Hamiltonian systems, Lagrangian tori, and Birkhoff's theorem. Math. Ann. 292 (1992), 619-627.
11. M. Coornaert, T. Delzant and A. Papadopoulos. Géométrie et Theorie de Groupes: Les Groups Hyperboliques de Gromov. Springer, 1990.
12. J. Denvir and R. S. MacKay. Consequences of contractible geodesies on surfaces. Trans. Amer. Math. Soc. 350 (1998), 4553-4568.
13. F. B. Fuller. On the surface of section and periodic trajectories. Am. J. Math. 87 (1965), 473-480.
14. E. Ghys and P. de la Harpe (Eds). Sur les Groupes Hyperboliques d'après Mikhael Gromov. Birkhäuser, 1990.
15. C. Golé. Periodic orbits for Hamiltonians in cotangent bundles. Trans. Amer. Math. Soc. 343 (1994), 327-347.
16. M. Gromov. Three remarks on geodesic dynamics and fundamental group. Preprint, SUNY at Stony Brook.
17. M. Gromov. Hyperbolic groups. Essays in Group Theory (MSRI Publications, 8). Ed. S. M. Gersten. Springer, 1987.
18. B. Hasselblat and A. Katok. Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, 1995.
19. A. Katok. Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Twist Mappings and Their Applications (I.M.A., 44). Eds R. McGehee and K. Meyer. Springer, 1992.
20. R. S. MacKay, J. D. Meiss and J. Stark. Converse KAM theory for symplectic twist maps. Nonlinearity 2 (1989), 555-570.
21. R. Mañé. Global variational methods in conservative dynamics. 18° Colóquio Brasileiro de Matemática. IMPA, 1991.
22. J. Mather. Action minimizing invariant measures for positive definite Lagrangian systems. Math. Z. 207 (1991), 169-207.
23. J. Mather. Variational constructions of connecting orbits. Ann. Inst. Fourier, Grenoble 43(5) (1993), 1349-1386.
24. J. D. Meiss. Symplectic maps, variational principles, and transport. Rev. Mod. Phys. 64(3) (1992), 795-848.
25. M. Morse. A fundamental class of geodesies on any closed surface of genus greater than one. Trans. Math. Soc. 26 (1924), 25-60.
26. J. Moser. Monotone twist mappings and the calculus of variations. Ergod. Th. & Dynam. Sys. 8* (1986), 199-214.
27. W. Parry. Topics in Ergodic Theory. Cambridge University Press, 1981.
28. M. Pollicott. Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds, (Lond. Math. Soc. Lecture Notes in Mathematics, 180). Cambridge University Press, 1993.