Abstract
We present a symplectic mapping model that is valid close to the 2:1 resonance in a Sun-Jupiter-asteroid system, for planar motion. The mapping is based on the averaged Hamiltonian close to this resonance, where an additional correction term has been introduced in order to restore the correct position and stability of the fixed points. The topology of the mapping is similar to that of the Poincaré map of the real system. The evolution of the eccentricity of the asteroid is presented and it is shown that for a large region of phase space there is a diffusion to very large values, leading to escape of the asteroid from the 2:1 resonance. There are however regions in phase space where the eccentricity remains bounded, in the framework of this model.
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© 1997 Springer Science+Business Media Dordrecht
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Hadjidemetriou, J.D., Lemaitre, A. (1997). Asteroid Motion Near the 2:1 Resonance: A Symplectic Mapping Approach. In: Dvorak, R., Henrard, J. (eds) The Dynamical Behaviour of our Planetary System. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5510-6_19
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DOI: https://doi.org/10.1007/978-94-011-5510-6_19
Publisher Name: Springer, Dordrecht
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