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Lyapunov and diffusion timescales in the Solar system 3. Chaos “due to encounters”. I. I. Shevchenko Pulkovo Observatory. Abstract.
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Lyapunov and diffusion timescales in the Solar system3. Chaos “due to encounters” I. I. Shevchenko Pulkovo Observatory
Abstract We consider chaos “due to encounters” in the dynamics of the Solar system bodies. This terminology is conventional, because the essential source of chaos is the same: interaction of resonances.
The encounter map Murray C.D., Dermott S.F. Solar SystemDynamics(1999).
The μ2/7 law Murray C.D., Dermott S.F. Solar SystemDynamics(1999).
The Kepler map The Kepler map was derived by Petrosky (1986) and Chirikov and Vecheslavov (1986) in the framework of the restricted three-body and four-body problems in order to describe the long-term chaotic orbital behaviour of Halley’s comet and, generally, that of the comets in nearly parabolic motion. It is a two-dimensional area-preserving map, describing a comet’s motion in terms of energy and time. Its second equation is based on Kepler’s third law, hence the name of the map. Since 1980s the Kepler map has become paradigmatic in a number of applications in celestial mechanics and in atomic physics. It represents an important kind of general separatrix maps.
The Kepler map • Petrosky, T.Y., Phys. Letters A117, 328 (1986). • Chirikov, B.V. and Vecheslavov, V.V., INP Preprint 86–184 (1986). • Petrosky, T.Y. and Broucke, R., Celest. Mech. 42, 53 (1988).