Abstract
We study some aspects of the restricted three-body problem when the mass parameter μ is sufficiently small. First, we describe the global flow of the two-body rotating problem, μ=0, and we use it for the analysis of the collision and parabolic orbits when μ≳0. Also we show that for any fixed value of the Jacobian constant and for any ε>0, there exists a μ0>0 such that if the mass parameter μ∈[0,μ0], then the set of bounded orbits which are not contained in the closure of the set of symmetric periodic orbits has Lebesgue measure less than ε.
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Llibre, J. On the restrited three-body problem when the mass parameter is small. Celestial Mechanics 28, 83–105 (1982). https://doi.org/10.1007/BF01230662
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DOI: https://doi.org/10.1007/BF01230662