Abstract
This paper attempts to give quantitative as well as qualitative answers to the question of the analogy between smooth potentials and N-body systems. A number of simulations were performed in both integrable and nonintegrable smooth environments and their frozen N-body analogues, and comparisons were made using a number of different tools. The comparisons took place on both statistical and pointwise levels. The results of this study suggest that microscopic chaos associated with discreteness effects is always present in N-body configurations. This chaos is different from the macroscopic chaos which is associated with the bulk potential and persists even for very large N. Although the Lyapunov exponents of orbits evolving in N-body environments do not decrease as N increases, comparisons associated with the statistical properties, as well as with the power spectra of the orbits, affirm the existence of the continuum limit.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Bennetin L. Galgani A. Giorgilli J. M. Strelcyn (1980) Meccanica 15 9 Occurrence Handle10.1007/BF02128236
G. Bertin (2000) Dynamics of Galaxies Cambridge University Press Cambridge
J. Binney S. Tremaine (1987) Galactic Dynamics Princeton University Press Princeton
Bohn, C. L., Kandrup, H. E. and Kishek, R. A.: 2001, In: C. M. Sazama (ed.), Proceedings of Snowmass 2001eConf C01/06/30, M302.
S. Chandrasekhar (1943a) Rev. Mod. Phys. 15 1 Occurrence Handle10.1103/RevModPhys.15.1
S. Chandrasekhar (1943b) Principles of Stellar Dynamics University of Chicago Chicago.
J. Goodman D. Heggie P. Hut (1993) Astrophys. J. 415 715 Occurrence Handle10.1086/173196
F. Hemsendorf D. Merritt (2002) Astrophys. J. 580 606 Occurrence Handle10.1086/343027
Hockney, R. W. and Eastwood, J. W.: 1988, Computer Simulation Using Particles A. Hilger, Philadelphia.
H. E. Kandrup (1989) Physica A 169 73 Occurrence Handle10.1016/0378-4371(90)90217-G
H.E. Kandrup (1998) Mon. Not. R. Astr. Soc. 301 960 Occurrence Handle10.1046/j.1365-8711.1998.02063.x
H.E. Kandrup I. V. Sideris (2001) Phys. Rev. E 64 056209 Occurrence HandleMR1869202
H.E. Kandrup I. V. Sideris (2002) Celestial Mech. Dyn. Astr 82 61 Occurrence Handle10.1023/A:1013859118402
H.E. Kandrup I.V. Sideris (2003) Astrophys. J. 585 244–250 Occurrence Handle10.1086/345948
H.E. Kandrup H. Smith (1991) Astrophys. J. 374 255 Occurrence Handle10.1086/170114
H.E. Kandrup I. V. Pogorelov I. V. Sideris (2000) Mon. Not. R. Astr. Soc. 311 719 Occurrence Handle10.1046/j.1365-8711.2000.03097.x
H.E. Kandrup I. V. Sideris C. L. Bohn (2004) Phys. Rev. Special Topics – Accelerators Beams 7 014202-1–014202-11
A. J. Lichtenberg M.A. Lieberman (1992) Regular and Chaotic Dynamics Springer Berlin
M.E. Mahon R. A. Abernathy H.E. Kandrup O. B. Bradley (1995) Mon. Not. R. Astr. Soc. 275 443
R.H. Miller (1964) Astrophys. J. 140 250 Occurrence Handle10.1086/147911
Miller, R. H.: 1964, Astrophys. J. 140, 250.
M. Tabor (1989) Chaos and Integrability in Nonlinear Dynamics Wiley New York
Valluri M. and Merritt, D.: 1999, In: R. Ruffini and V. G. Gurzadyan (eds), The Chaotic UniverseWorld Scientific, New York.
N. G. van Kampen (1981) Stochastic Processes in Physics and Chemistry North Holland Amsterdam
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sideris, I.V. The validity of the continuum limit in the gravitational N-body problem. Celestial Mech Dyn Astr 90, 147–162 (2004). https://doi.org/10.1007/s10569-004-6443-5
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10569-004-6443-5