Geometry of chaos in models of stellar dynamics

Celestial Mechanics and Dynamical Astronomy

Volumn 83, Issue 1-4, 2002, Pages 171-190

  Ciraolo, Guido ^a   Pettini, Marco ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b INAF OSSERVATORIO ASTROFISICO DI ARCETRI   (Italy)

Author keywords

Hamiltonian chaos; Stellar dynamics

Indexed keywords

EID: 0036374048     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020195100161     Document Type: Article

References (21)

1. Binney, J. and Tremaine, S.: 1987, Galactic Dynamics, Princeton University Press, Princeton, N.J., Chapter 3.
2. Casetti, L.: 1995, Efficient symplectic algorithms for numerical simulations of Hamiltonian flows, Phys. Scr. 51, 29-34.
3. Casetti, L., Cerruti-Sola, M., Pettini, M. and Cohen, E.G.D.: 1997, The Fermi-Pasta-Ulam problem revisited: Stochasticity thresholds in nonlinear Hamiltonian systems, Phys. Rev. E 55, 6566-6574.
4. Casetti, L., Clementi, C. and Pettini, M.: 1996, Riemannian theory of Hamiltonian chaos and Lyapunov exponents, Phys. Rev. E 54, 5969-5984.
5. Casetti, L., Pettini, M. and Cohen, E.G.D.: 2000, Geometric approach to Hamiltonian dynamics and statistical mechanics, Phys. Rep. 337, 237-341.
6. Cerruti-Sola, M. and Pettini, M.: 1996, Geometric description of chaos in two degrees of freedom Hamiltonian systems, Phys. Rev. E 53, 179-188.
7. Cerruti-Sola, M., Franzosi, R. and Pettini, M.: 1997, Lyapunov exponents from geodesic spread in configuration space, Phys. Rev. E 56, 4872-4875.
8. Contopoulos, G. and Barbanis, B.: 1989, Lyapunov characteristic numbers and the structure of phase space, Astron. & Astrophys. 222, 329-343.
9. Contopoulos, G.: 1986, Qualitative changes in 3-dimensional dynamical systems, Astron. & Astrophys. 161, 244-256.
10. Contopoulos, G.: 1988, In: A.E. Roy (ed.), Long Term Dynamical Behaviour of Natural and Artificial N: Body Systems, 301.
11. Contopoulos, G. and Grosbøl, P.: 1989, Orbits in barred galaxies, Astron. Astrophys. Rev. 1, 261-289.
12. Contopoulos, G. and Magnenant, P.: 1985, Simple three dimensional periodic orbits in a galactic-type potential, Cel. Mech. 37, 387-414.
13. Do Carmo, M.P.: 1992, Riemannian Geometry, Birkhäuser, Boston.
14. Eisenhart, L.P.: 1929, Dynamical Trajectories and Geodesics, Ann. Math. 30, 591-606.
15. Guckenheimer, J. and Holmes, P.J.: 1983, Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields, Springer-Verlag, New York.
16. Hénon, M. and Heiles, C.: 1964, The applicability of the third integral of motion: some numerical experiments, Astron. J. 69, 73-79.
17. Henrard, J. and Ferraz-Mello, S. (eds): 1999, Cel. Mech. 73, Nos. 1-4, Special Issue on impact of modern dynamics in astronomy.
18. Kandrup, H.E., Sideris, I.V. and Bohn, C.L.: 2001, Chaos, ergodicity, and the thermodynamics of lower-dimensional Hamiltonian systems, astro-ph/0108038.
19. Pettini, M.: 1993, Geometrical hints for a non perturbative approach to Hamiltonian dynamics, Phys. Rev. E 47, 828-850.
20. Pettini, M. and Valdettaro, R.: 1995, On the Riemannian description of chaotic instability in Hamiltonian dynamics, Chaos 5, 646-652.
21. Poincaré, H.: 1892, Les Méthodes Nouvelles de la Mécanique Celeste, Gauthier-Villars, Paris.