Collective geodesic flows

Annales de l'Institut Fourier

Volumn 53, Issue 1, 2003, Pages

  Butler, L T ^a   Paternain, G P ^b  

^a NORTHWESTERN UNIVERSITY   (United States)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Collective geodesic flows; Melnikov integral; Semi simple Lie algebras Moment map; Topological entropy

Indexed keywords

EID: 0038166036     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1944     Document Type: Article

References (28)

1. M. ADLER, P. VAN MOERBEKE, Geodesic flow on SO(4) and the intersection of quadrics, Proc. Nat. Acad. Sci. U.S.A., 81 (1984), 4613-4616.
2. M. ADLER & P. VAN MOERBEKE, The algebraic integrability of geodesic flow on so(4), Invent. Math., 67 (1982), 297-331.
3. V. I. ARNOLD (Ed.), Dynamical Systems III, Encyclopaedia of Mathematical Sciences, Springer Verlag, Berlin, 1988.
4. O. I. BOGOYAVLENSKY, Integrable Euler equations on so(4) and their physical applications, Comm. Math. Phys., 93 (1984), 417-436.
5. A.V. BOLSINOV & A.T. FOMENKO, Orbital isomorphism between two classical integrable systems. The Euler case and the Jacobi problem, Lie groups and Lie algebras, 359-382, Math. Appl., 433, Kluwer Acad. Publ., Dordrecht, 1998.
6. R. BOWEN, Entropy for Group Endomorphisms and Homogeneous spaces, Trans. of Am. Math. Soc., 153 (1971), 401-414.
7. K. BURNS & H. WEISS, A geometric criterion for positive topological entropy, Comm. Math. Phys., 172 (1995), 95-118.
8. V. GUILLEMIN & S. STERNBERG, Symplectic techniques in physics, Cambridge University Press, Cambridge, 1984.
9. V. GUILLEMIN & S. STERNBERG, The moment map and collective motion, Ann. Physics, 127 (1980), 220-253.
10. L. HAINE, The algebraic complete integrability of geodesic flow on so(N), Comm. Math. Phys., 94 (1984) 271-287.
11. H. HANCOCK, Lectures on the Theory of Elliptic Functions, Dover, New York, 1909 (reprint 1958).
12. B. HASSELBLATT & A. KATOK, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications 54 Cambridge University Press (1995).
13. S. HELGASON, Differential geometry, Lie groups, and symmetric spaces, American Mathematical Society, Providence, RI, 2001. Corrected reprint of the 1978 original.
14. P. HOLMES & J. MARSDEN, Horseshoes and Arnol'd diffusion for Hamiltonian systems on Lie groups, Indiana Univ. Math. J., 32 (1983), 273-309.
15. W. KLINGENBERG, Riemannian Geometry, De Gruyter, Berlin-New York, 1982.
16. V.V. KOZLOV & D.A. ONISHCHENKO, Nonintegrability of Kirchhoff's equations, (Russian) Dokl. Akad. Nauk SSSR, 266 (1982), 1298-1300.
17. S. V. MANAKOV, A remark on the integration of the Eulerian equations of the dynamics of an n-dimensional rigid body, Funkcional. Anal, i Priložen., 10 (1976), 93-94.
18. R. MAÑÉ, On the topological entropy of geodesic flows, J. Diff. Geom., 45 (1997), 74-93.
19. A. S. MIŠČENKO, Integrals of geodesic flows on Lie groups, Funkcional. Anal. I Priložen., 4 (1970), 73-77.
20. A. S. MlŠČENKO & A. T. FOMENKO, The integration of Euler equations on a semisimple Lie algebra, Dokl. Akad. Nauk SSSR, 231 (1976), 536-538.
21. A. S. MIŠČENKO & A. T. FOMENKO, A generalized Liouville method for the integration of Hamiltonian systems, Funkcional. Anal, i Priložen., 12 (1978), 46-56.
22. O.E. OREL, Euler-Poinsot dynamical systems and geodesic flows of ellipsoids: topologically nonconjugation, Tensor and vector analysis, 76-84, Gordon and Breach, Amsterdam, 1998.
23. C. ROBINSON, Horseshoes for autonomous Hamiltonian systems using the Melnikov integral, Ergodic Theory Dynam. Systems, 8* (Charles Conley Memorial Issue) (1988) 395-409.
24. A. THIMM, Integrable geodesic flows on homogeneous spaces, Ergod. Th. And Dyn. Syst., 1 (1981), 495-517.
25. A.P. VESELOV, Conditions for the integrability of Euler equations on so(4), (Russian) Dokl. Akad. Nauk SSSR, 270 (1983), 1298-1300.
26. P. WALTERS, An introduction to ergodic theory, Graduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg-Berlin (1982).
27. A. WEINSTEIN, The local structure of Poisson manifolds, J. Differential Geom., 18 (1983) 523-557.
28. Z. XIA, Homoclinic points and intersections of Lagrangian submanifolds, Discrete Contin. Dynam. Systems, 6 (2000), 243-253.