Mathematics – Dynamical Systems
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008dda....39.0803n&link_type=abstract
American Astronomical Society, DDA meeting #39, #8.03
Mathematics
Dynamical Systems
Scientific paper
Sussman and Wisdom [1992] found that the outer Solar System is chaotic with a Lyapunov time of seven to twenty million years. The shortness of this Lyapunov time stimulated research on the long-term behaviour of the outer Solar System. Three important results have emerged from this research. First, for long-term simulations using symplectic methods, the timestep must be noticeably smaller than previously thought to ensure qualitative information such as the existence of chaos is correct. For example, Grazier et al. (1999) using more accurate integration approach observed that chaotic behavior disappeared when a sufficiently small time step was employed. Second, changes in the initial conditions of the order of the uncertainty in the DE405 ephemeris can create or remove chaos. Third, our models of the outer Solar System may be insufficiently robust to provide reliable information about the long-term behavior. Another aspect of the modelling that must be considered is that any realistic model of the Solar System will be a high dimensional dynamical system. This high dimensionality means the standard definitions and techniques used in chaos theory are not immediately applicable. This complication has been observed in other well-known dynamical systems, such as the Fermi-Pasta-Ulam problem (Berman and Izrailev, 2005). We show that these insights may be relevant to the simple outer solar system that is often employed, but leaves open the question of the behavior of our solar system complicated by other influences ranging from the presence of small bodies to other dynamical effects.
G.P. Berman and F.M. Izrailev (2005) Chaos 15, 015104-1-18
K.R. Grazier, W.I. Newman, W.M. Kaula, and J.M. Hyman (1999). Icarus 140, 341-352.
G.J. Sussman and J. Wisdom (1992). Science 257, 56-62.
Grazier Kevin R.
Newman William I.
Sharp P.
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