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Chaotic structure of the capture domain. (English) Zbl 1325.70037

Érdi, Bálint (ed.) et al., International conference on actual problems in celestial mechanics and dynamical astronomy, Cluj-Napoca, Romania, May 25–27, 2006. Cluj-Napoca: Presa UniversitarăClujeană/ Cluj University Press (ISBN 978-973-610-555-5/pbk). Publications of the Astronomy Department of the Eötvös University 19, 237-245 (2007).
Summary: The ballistic capture is the phenomenon, where a massless particle changes its Kepler-energy around one of the primaries from positive to negative. Belbruno used the time as measure of the capture. In this paper we study the phenomenon of capture by using the variation of the polar angle of the relative position vector of the small body around the capturing planet. We defined the capture effect of the planet to the captured body, as the variation of this polar angle during the capture. Several zones are determined around the capturing body, in which, for a given velocity, the capture take place. These regions are called capture domains. In this paper we show that the capture domain is a subset of scattering region and chaos in the capture domain is transient.
For the entire collection see [Zbl 1117.70002].

MSC:

70F15 Celestial mechanics
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
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