Shadowing high-dimensional Hamiltonian systems: The gravitational N-body problem

Physical Review Letters

Volumn 90, Issue 5, 2003, Pages

  Hayes, Wayne B ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHAOS THEORY; COMPUTER SIMULATION; GRAPH THEORY; HAMILTONIANS; LYAPUNOV METHODS; MATHEMATICAL MODELS; OPTIMIZATION; PROBABILITY DENSITY FUNCTION; STATISTICAL METHODS; VECTORS;

GRAVITATIONAL N-BODY PROBLEM; HIGH-DIMENSIONAL HAMILTONIAN SYSTEM; SHADOWING;

ASTROPHYSICS;

EID: 0037422921     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. Proceedings of the 12th "Kingston Meeting": Computational Astrophysics, edited by D. A. Clarke and M. J. West, ASP Conference Series Vol. 123 (Astronomical Society of the Pacific, San Francisco, CA, 1997).
2. E. Bertschinger, Annu. Rev. Astron. Astrophys. 36, 599 (1998).
3. J. Goodman, D. C. Heggie, and P. Hut, Astrophys. J. 415, 715 (1993).
4. S. Dawson, C. Grebogi, T. Sauer and J. A. Yorke, Phys. Rev. Lett. 73, 1927 (1994).
5. T. Sauer, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 79, 59 (1997).
6. T. D. Sauer, Phys. Rev. E 65, 036220 (2002).
7. J. D. Farmer and J. J. Sidorowich, Physica (Amsterdam) 47D, 373 (1991).
8. S. T. Fryska and M. A. Zohdy, Phys. Lett. A 166, 340 (1992).
9. R. M. Corless, Comput. Math. Appl. 28, 107 (1994).
10. This question is not unique to shadowing; e.g., is the exact solution to a nearby Hamiltonian problem produced by a symplectic integrator typical nearby problems?
11. C. Grebogi, S. M. Hammel, J. A. Yorke, and T. Sauer, Phys. Rev. Lett. 65, 1527 (1990).
12. G. D. Quinlan and S. Tremaine, Mon. Not. R. Astron. Soc. 259, 505 (1992).
13. D. C. Heggie and R. D. Mathieu, in The Use of Supercomputers in Stellar Dynamics, edited by P. Hut and S. L. W. McMillan (Springer-Verlag, Berlin, 1986), pp. 233-235.
14. A. C. Hindmarsh, ACM-SIGNUM Newsletter 15, 10 (1980).
15. J. A. Rice, Mathematical Statistics and Data Analysis (Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1988).
16. J. Binney and S. Tremaine, Galactic Dynamics, Princeton Series in Astrophysics (Princeton University Press, Princeton, NJ, 1987).
17. This effect will be quantified in an upcoming paper.
18. W. Hayes, Master's thesis, University of Toronto, 1995.