2009
DOI: 10.1007/s00220-009-0769-5
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On Action-Minimizing Retrograde and Prograde Orbits of the Three-Body Problem

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Cited by 31 publications
(41 citation statements)
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“…Figure 1 shows some action-minimizing retrograde orbits with action lower than all Euler solutions. See [4,5] for a rigorous existence proof for such orbits. The upper left orbit was first numerically obtained by Hénon [11].…”
Section: Some Numerical Resultsmentioning
confidence: 99%
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“…Figure 1 shows some action-minimizing retrograde orbits with action lower than all Euler solutions. See [4,5] for a rigorous existence proof for such orbits. The upper left orbit was first numerically obtained by Hénon [11].…”
Section: Some Numerical Resultsmentioning
confidence: 99%
“…However, determining the braid types of the solutions (other than relative equilibria) obtained in Theorem 2.2 is a non-trivial task. For most choices of masses in the three-body problem, existence of solutions in H φ,T,R,B −1 (that is, the space of retrograde paths in H φ,T,R ) with φ away from zero was proved in [4] (see also [5]). We conjecture that, for any n, the action-minimizing solutions obtained in Theorem 2.2 for φ ∈ (φ c , π] have non-trivial braid types.…”
Section: Bifurcation From Euler-moulton Relative Equilibriamentioning
confidence: 99%
“…In this section, we obtain lower bounds of actions when P Q i ([0, 1]) (i = 1, 2) have boundary collisions. We first introduce a theorem of Chen [5,7,11] which estimates the Keplerian action functional. Given θ ∈ (0, π], T > 0, consider the following path spaces:…”
Section: Lower Bounds Of Action Of Paths With Boundary Collisionsmentioning
confidence: 99%
“…He introduced a binary decomposition method [6], such that the standard action functional can be decomposed to the sum of several Keplerian action functionals. A nice lower bound of action of all collision paths can be obtained by applying an estimate of the Keplerian action functionals [5,7]. Indeed, this binary decomposition method works not only for the three-body problem, but for all the N-body problems.…”
Section: Introductionmentioning
confidence: 99%
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