Nonlinear Sciences – Chaotic Dynamics
Scientific paper
May 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995aas...186.1304n&link_type=abstract
American Astronomical Society, 186th AAS Meeting, #13.04; Bulletin of the American Astronomical Society, Vol. 27, p.829
Nonlinear Sciences
Chaotic Dynamics
Scientific paper
The relationship between symplectic properties and numerical accuracy is investigated using the dynamics of the Jovian planets as an example. What are the properties of symplectic integrators, including both their benefits and limitations, and how do they contrast with classical integration schemes? The dynamics of the Wisdom-Holman mapping appears to be different than that provided by very high order multi-step integrators. We will clarify the nature of such differences and how they affect orbital trajectories using elementary results in bifurcation theory. The significance of these differences regarding chaotic dynamics in the Solar system is discussed. Can the distortion of the dynamics by the Wisdom-Holman mapping lead to artificial separatrices and separatrix crossings---and to incorrect physical conclusions regarding the dynamics?
Grazier Kevin R.
Kaula William M.
Newman William I.
Varadi Ferenc
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