Invariant fibrations of geodesic flows

Topology

Volumn 44, Issue 4, 2005, Pages 769-789

  Butler, Leo T ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

3 manifolds; Geodesic flows; Integrable systems; Liouville foliations; Momentum map; Nonintegrability

Indexed keywords

EID: 17644363295     PISSN: 00409383     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.top.2005.01.004     Document Type: Article

References (32)

1. O.I. Bogoyavlenskij Theory of tensor invariants of integrable Hamiltonian systems. I. Incompatible Poisson structures Comm. Math. Phys. 180 3 1996 529-586
2. O.I. Bogoyavlenskij Theory of tensor invariants of integrable Hamiltonian systems. II. Theorem on symmetries and its applications Comm. Math. Phys. 184 2 1997 301-365
3. S.V. Bolotin Nonintegrability of the problem of n centers for n>2 Vestnik Moskov. Univ. Ser. I Mat. Mekh. 3 1984 65-68
4. S.V. Bolotin Homoclinic orbits of geodesic flows on surfaces Russian J. Math. Phys. 1 3 1993 275-288
5. S. Bolotin P. Negrini A variational criterion for nonintegrability Russian J. Math. Phys. 5 4 1997 415-436
6. A.V. Bolsinov B. Ǐovanovich Integrable geodesic flows on homogeneous spaces Mat. Sb. 192 7 2001 21-40
7. A.V. Bolsinov I.A. Taǐmanov Integrable geodesic flows on suspensions of automorphisms of tori Tr. Mat. Inst. Steklova 231 2001 46-63
8. A.V. Bolsinov I.A. Taǐmanov Integrable geodesic flows with positive topological entropy Invent. Math. 140 3 2000 639-650
9. L.T. Butler A new class of homogeneous manifolds with Liouville-integrable geodesic flows C. R. Math. Acad. Sci. Soc. R. Can. 21 4 1999 127-131
10. L.T. Butler Integrable geodesic flows on n-step nilmanifolds J. Geom. Phys. 36 3,4 2000 315-323
11. L.T. Butler New examples of integrable geodesic flows Asian J. Math. 4 3 2000 515-526
12. L.T. Butler Integrable geodesic flows with wild first integrals the case of two-step nilmanifolds Ergodic Theory Dyn. Systems 23 3 2003 771-797
13. K. Dekimpe, Almost-Bieberbach Groups: Affine and Polynomial Structures, Lecture Notes in Mathematics, vol. 1639, Springer, Berlin, 1996.
14. N. Desolneux-Moulis Dynamique des systèmes hamiltoniens complètement intégrables sur les variétés compactes, in: Géométrie symplectique et mécanique La Grande Motte, 1988 1990 Springer Berlin 75-83
15. B. Evans L. Moser Solvable fundamental groups of compact 3-manifolds Trans. Amer. Math. Soc. 168 1972 189-210
16. M. Giaquinta S. Hildebrandt Calculus of Variations vols. I,II 1996 Springer Berlin
17. M. Gromov Groups of polynomial growth and expanding maps Inst. Hautes tudes Sci. Publ. Math. 53 1981 53-73
18. J. Hempel W. Jaco Fundamental groups of 3-manifolds which are extensions Ann. Math. 95 2 1972 86-98
19. H. Ito Action-angle coordinates at singularities for analytic integrable systems Math. Z. 206 3 1991 363-407
20. V. Jurdjevic Geometric Control Theory 1997 Cambridge University Press Cambridge
21. V.V. Kozlov Topological obstacles to the integrability of natural mechanical systems Dokl. Akad. Nauk SSSR 249 6 1979 1299-1302
22. V.V. Kozlov Symmetries, Topology and resonances in Hamiltonian Mechanics 1996 Springer Berlin
23. S. Lojasiewicz Triangulation of semi-analytic sets Ann. Scuola Norm. Sup. Pisa 18 3 1964 449-474
24. J.R. Munkres Elements of Algebraic Topology 1984 Addison-Wesley Reading, MA
25. G.P. Paternain On the topology of manifolds with completely integrable geodesic flows Ergodic Theory Dynamical Systems 12 1 1992 109-121
26. G.P. Paternain Multiplicity two actions and loop space homology Ergodic Theory Dynamical Systems 13 1 1993 143-151
27. G.P. Paternain On the topology of manifolds with completely integrable geodesic flows. II J. Geom. Phys. 13 3 1993 289-298
28. H. Putz Triangulation of fibre bundles Canad. J. Math. 19 1967 499-513
29. P. Scott The geometries of 3-manifolds Bull. London Math. Soc. 15 5 1983 401-487
30. I.A. Taǐmanov Topological obstructions to the integrability of geodesic flows on nonsimply connected manifolds Izv. Akad. Nauk SSSR Ser. Mat. 51 2 1987 429-435, 448
31. I.A. Taǐmanov Topology of Riemannian manifolds with integrable geodesic flows Trudy Mat. Inst. Steklov. 205 1994 150-163
32. G.W. Whitehead Elements of Homotopy Theory 1978 Springer New York