Hyperbolic dynamics of Euler-Lagrange flows on prescribed energy levels

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1. [1] V.I. ARNOLD, A.B. GIVENTAL. - Symplectic Geometry, Dynamical Systems IV, Encyclopaedia of Mathematical Sciences, Springer Verlag: Berlin 1990 Zbl0778.00008MR1042758
2. [2] V. BANGERT. - Minimal geodesics, Ergod. Th. and Dynam. Sys. 10 ( 1989) 263-286. Zbl0676.53055MR1062758
3. [3] Y. BENOIST, P. FOULON, F. LABOURIE. - Flots d'Anosov a distributions stable et inestable différentiables, Journal of the AMS 5 ( 1992) 33-74. Zbl0759.58035MR1124979
4. [4] G. BESSON, G. COURTOIS, S. GALLOT. - Entropies et rigidités desespaces localement symétriques de courbure strictement négative, Geom. Funct. Anal. 5 ( 1995) 731-799. Zbl0851.53032MR1354289
5. [5] M. BLALY, L. POLTEROVICH. - Hamiltonian diffeomorphisms and Lagrangian distributions, Geom. Funct. Anal. 2 ( 1992) 173-210 Zbl0761.58010MR1159829
6. [6] P. BOYLAND, C. GOLÉ. - Lagrangian systems on hyperbolic manifolds, preprint. Zbl0971.37017MR1721614
7. [7] M. BRUNELLA. - Expansive flows on Seifert manifolds and torus bundles, Bulletin of the Brazilian Math. Society 24 ( 1993) 89-104. Zbl0786.58029MR1224301
8. [8] C. CAMACHO, A. LINS NETO. - Geometric theory of foliations, Birkhauser Boston, Inc., Boston, Mass., 1985. Zbl0568.57002MR824240
9. [9] G. CONTRERAS, J. DELGADO, R. ITURRLAGA. - Lagrangian flows: the dynamics of globally minimizing orbits II, to appear in Bulletin of the Brazilian Math. Society, preprint available via internet at "http://www.ma.utexas.edu/mp-arc". Zbl0892.58065
10. [10] G. CONTRERAS, R. ITURRIAGA. - Convex Hamiltonians without conjugate points, to appear in Ergod.Th and Dynam. Sys., preprint available via internet at "http:// www.ma.utexas.edu/mp-arc" Zbl1044.37046MR1709426
11. [11] G. CONTRERAS, R. ITURRIAGA, G.P. PATERNAIN, M. PATERNAIN. - Lagrangian graphs, minimizing measures and Manés critical values, preprint 1997 Zbl0920.58015
12. [12] M.J. DIAS CARNEIRO. - On minimizing measuresof the action of autonomous Lagrangians, Nonlineariry 8 ( 1995) 1077-1085. Zbl0845.58023MR1363400
13. [13] J.J. DUISTERMAAT. - On the Morse index in variational calculus, Adv. in Math. 21 ( 1976) 173-195. Zbl0361.49026MR649277
14. [14] A. FATHI. - Théorème KAM faible et Théorie de Mather sur les systems Lagrangiens, C.R. Acad. Sci. Paris, t. 324, Sériel ( 1997) 1043-1046. Zbl0885.58022MR1451248
15. [15] A. FATHI. - Solutions KAM faibles conjuguées et barrières de Peierls, preprint 1997. Zbl0943.37031MR1473840
16. [16] R. FERES, A. KATOK. - Invariant tensor fields of dynamical systems with pinched liapunov exponents and rigidity of geodesic flows, Ergod. Th and Dynam. Sys. 9 ( 1989) 427-432. Zbl0667.58050MR1016661
17. [17] R. FERES, A. KATOK. - Anosov flows with smooth foliations and rigidity of geodesie flows in three- dimensional manifolds of negative curvarture, Ergod. Th and Dynam. Sys. 10 ( 1990) 657-670. Zbl0729.58039MR1091420
18. [18] R. FERES. - Geodesic flows on manifolds with negative with smooth horospheric foliations, Ergod. Th and Dynam. Sys. 11 ( 1991) 653-686. Zbl0727.58035MR1145615
19. [19] L. FLAMINIO. - Local entropy rigidity for hyperbolic manifolds, Comm. in Analysis and Geom. 4 ( 1995) 555-596. Zbl0852.58068MR1371210
20. [20] P. FOULON. - Feuilletages des sphères et dynamiques Nord-Sud, C.R. Acad. Sci Paris, t. 318, Série I ( 1994) 1041-1042. Zbl0809.57019MR1281888
21. [21] E. GHYS. - Flots d'Anosov sur les3-variétés fibrées en cercles, Ergod. Th and Dynam. Sys. 4 ( 1984)67-80. Zbl0527.58030MR758894
22. [22] E. GHYS. - Flots d'Anosov dont les feuilletages stables sont différentiables, Ann. Sci. École Norm. Sup. 20 ( 1987) 251-270. Zbl0663.58025MR911758
23. [23] U. HAMENSTÄDT. - Invariant two-forms for geodesic flows, Math. Ann. 301 ( 1995) 677-698. Zbl0821.58033MR1326763
24. [24] B. HASSELBLATT. - Regularityof the Anosov splitting and of horospherical foliations, Ergod. Th and Dynam. Sys. 14 ( 1994) 645-666. Zbl0821.58032MR1304137
25. [25] G.A. HEDLUND. - Geodesics on a two-dimensional Riemannian manifold with periodic coefficients, Ann. of Math. 33 ( 1932) 719-739. Zbl0006.32601MR1503086JFM58.1256.01
26. [26] K. HIRAIDE. - Expansive homeomorphisms of compact surfaces are Pseudo-Anosov, Osaka J. Math. 27 ( 1990) 117-162. Zbl0713.58042MR1049828
27. [27] M. HIRSCH, C. PUGH. - Smoothness of horocycle foliations, J. Diff. Geom. 10 ( 1975) 225-238. Zbl0312.58008MR368077
28. [28] S. HURDER, A. KATOK. - Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Publ. Math. IHES 72 ( 1990) 5-61 Zbl0725.58034MR1087392
29. [29] T. INABA, S. MATSUMOTO. - Nonsingular expansive flows on 3-manifolds and foliations with circle prong singularities, Japan J. of Math. 16 ( 1990) 329-340. Zbl0729.58046MR1091166
30. [30] M. KANAI. - Geodesic flows on negatively curved manifolds with smooth stable and unstable foliations, Ergod. Th and Dynam. Sys. 8 ( 1988) 215-240. Zbl0634.58020MR951270
31. [31] W. KLINGENBERG. - Riemannian manifolds with geodesic flows of Anosov type, Ann. of Math., 99 ( 1974) 1-13. Zbl0272.53025MR377980
32. [32] J. LEWOWICZ. - Expansive homeomorphisms on surfaces, Bulletin of the Brazilian Math. Society Vol 201 ( 1989)113-133. Zbl0753.58022MR1129082
33. [33] R. MAÑÉ. - On a theorem of Klingenberg, Dynamical Systems and Bifurcation Theory, M. Camacho, M. Pacifico and F.Takens eds, Pitman Research Notes in Math. 160 ( 1987),319-345. Zbl0633.58022MR907897
34. [34] R. MANÉ. - Global variational methods in conservative dynamics, 18 Colóquio Brasileiro de Maternatica.IMPA, 1991. 
35. [35] R. MANÉ. - Lagrangian flows: the dynamics ofglobally minimizing orbits, International Congress on Dynamical Systems in Montevideo (a tribute to Ricardo Mafié), F.Ledrappier, J. Lewowicz, S. Newhouse eds, Pitman Research Notes in Math. 362 ( 1996) 120-131. Zbl0870.58026MR1460800
36. [36] R. MANÉ. - Generic properties and problems of minimizing measures of Lagrangian systems, Nonlinearity 9 ( 1996) 273-310. Zbl0886.58037MR1384478
37. [37] J. MATHER. - Action minimizing measures for positive definite Lagrangian systems, Math. Z. 207 ( 1991) 169-207. Zbl0696.58027MR1109661
38. [38] J. MATHER. - Variational construction of connecting orbits, Ann. Inst Fourier 43 ( 1993) 1349-1386. Zbl0803.58019MR1275203
39. [39] M. MORSE. - A fondamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc. 26 ( 1924) 25-60. Zbl50.0466.04MR1501263JFM50.0466.04
40. [40] G.P. PATERNAIN, M. PATERNAIN. - On Anosou Energy Levels of Convex Hamiltonian Systems, Math. Z. 217 ( 1994) 367-376. Zbl0820.58022MR1306666
41. [41] G.P. PATERNAIN, M. PATERNAIN. - Expansivity for optical Hamiltonian systems with two degrees offreedom, C.R. Acad. Sci. Paris, t. 316, Série I ( 1993) 837-841. Zbl0790.58030MR1218272
42. [42] G. P. PATERNAIN, M. PATERNAIN. - Anosov geodesic flows and twisted symplectic structures, International Congress on Dynamical Systems in Montevideo (a tribute to Ricardo Marié), F. Ledrappier, J. Lewowicz, S. Newhouse eds, Pitman Research Notes in Math. 362 ( 1996) 132-145. Zbl0868.58062MR1460801
43. [43] G. P. PATERNAIN, M. PATERNAIN. - First derivative of topological entropy for Anosov geodesic flows in the presence of magnetic fields, Nonlinearity 10 ( 1997) 121-131. Zbl0907.58053MR1430743
44. [44] G. P. PATERNAIN, M. PATERNAIN. - Critical values of autonomous Lagrangian systems, Comment. Math. Helvetici 72 ( 1997), preprint available via internet at http://www.cmat.edu.uy/-gabriel". Zbl0921.58017MR1476061
45. [45] G. P. PATERNAIN. - On Anosov energy levels of Hamiltonians on twisted cotangent bundles, Bulletin of the Brazilian Math. Society Vol 25 2 ( 1994) 207-211. Zbl0829.58018MR1306561
46. [46] G. P. PATERNAIN. - On the regularity of the Anosov splitting for twisted geodesic flows, to appear in Math. Res. Lett., preprint available via internet at "http://www.cmat.edu.uy/-gabriel". Zbl0901.58017MR1492126
47. [47] M. PATERNAIN. - Expansive geodesic flows on surfaces, Ergod. Th and Dynam. Sys. 13 ( 1993) 153-165. Zbl0781.58033MR1213085
48. [48] M. PATERNAIN. - Expansive flows and the fondamental group, Bulletin of the Brazilian Math. SocietyVol 24 2 ( 1993)179-199. Zbl0796.58040MR1254982
49. [49] J. F. PLANTE. - Anosov flows, Amer. J. of Math. 94 ( 1972) 729-754 Zbl0257.58007MR377930
50. [50] J. F. PLANTE. - Homology of closed orbits of Anosov flows, Proc. of the A.M.S. 37 ( 1973) 297-300. Zbl0249.58012
51. [51] R. SCHWARTZMANN. - Asymptotic cycles, Ann. of Math. (2) 66 ( 1957) 270-284. Zbl0207.22603