Dynamics in first-order mean motion resonances: analytical study of a simple model with stochastic behaviour. (arXiv:1812.07773v1 [physics.space-ph])
<a href="http://arxiv.org/find/physics/1/au:+Efimov_S/0/1/0/all/0/1">Sergey Efimov</a>, <a href="http://arxiv.org/find/physics/1/au:+Sidorenko_V/0/1/0/all/0/1">Vladislav Sidorenko</a>

We examine a 2DOF Hamiltonian system, which arises in study of first-order
mean motion resonance in spatial circular restricted three-body problem
“star-planet-asteroid”, and point out some mechanisms of chaos generation.
Phase variables of the considered system are subdivided into fast and slow
ones: one of the fast variables can be interpreted as resonant angle, while the
slow variables are parameters characterizing the shape and orientation of the
asteroid’s orbit. Averaging over the fast motion is applied to obtain evolution
equations which describe the long-term behavior of the slow variables. These
equations allowed us to provide a comprehensive classification of the slow
variables’ evolution paths. The bifurcation diagram showing changes in the
topological structure of the phase portraits is constructed and bifurcation
values of Hamiltonian are calculated. Finally, we study properties of the chaos
emerging in the system.

We examine a 2DOF Hamiltonian system, which arises in study of first-order
mean motion resonance in spatial circular restricted three-body problem
“star-planet-asteroid”, and point out some mechanisms of chaos generation.
Phase variables of the considered system are subdivided into fast and slow
ones: one of the fast variables can be interpreted as resonant angle, while the
slow variables are parameters characterizing the shape and orientation of the
asteroid’s orbit. Averaging over the fast motion is applied to obtain evolution
equations which describe the long-term behavior of the slow variables. These
equations allowed us to provide a comprehensive classification of the slow
variables’ evolution paths. The bifurcation diagram showing changes in the
topological structure of the phase portraits is constructed and bifurcation
values of Hamiltonian are calculated. Finally, we study properties of the chaos
emerging in the system.

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