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Tanikawa, Kiyotaka; Umehara, Hiroaki

doi:10.1023/a:1008301405839

Cited by 19 publications

(9 citation statements)

References 11 publications

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“…In addition to this series of arcs, other series of zones with more complex structure are also observed, in which the triple systems also decay over comparatively short times after a small number of triple encounters. The structures found correspond qualitatively to zones of departure after the first, second, and third triple encounter found by Tanikawa and Umehara [17]. Similar structures in the domain D also arose in other studies of the free-fall three-body problem [18,19].…”

Section: Resultssupporting

confidence: 84%

The decay of triple systems

Martynova

Орлов

2014

Astron. Rep.

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Numerical simulations have been carried out in the general three-body problem with equal masses with zero initial velocities, to investigate the distribution of the decay times T based on a representative sample of initial conditions. The distribution has a power-law character on long time scales, f (T ) ∝ T −α , with α = 1.74. Over small times T < 30T cr (T cr is the mean crossing time for a component of the triple system), a series of local maxima separated by about 1.0T cr is observed in the decay-time distribution. These local peaks correspond to zones of decay after one or a few triple encounters. Figures showing the arrangement of these zones in the domain of the initial conditions are presented.

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Section: Resultssupporting

confidence: 84%

The decay of triple systems

Martynova

Орлов

2014

Astron. Rep.

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“…Oscillatory sequences directly specify a group of oscillatory orbits ͑see Ref. 12 for oscillatory orbits in the planar prob-lem͒. Consider transitions I 5 I 7 .…”

Section: Periodic Sequences and Periodic Orbitsmentioning

confidence: 99%

One-dimensional three-body problem via symbolic dynamics

Tanikawa

Mikkola

2000

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Symbolic dynamics is applied to the one-dimensional three-body problem with equal masses. The sequence of binary collisions along an orbit is expressed as a symbol sequence of two symbols. Based on the time reversibility of the problem and numerical data, inadmissible (i.e., unrealizable) sequences of collisions are systematically found. A graph for the transitions among various regions in the Poincare section is constructed. This graph is used to find an infinite number of periodic sequences, which implies an infinity of periodic orbits other than those accompanying a simple periodic orbit called the Schubart orbit. Finally, under reasonable assumptions on inadmissible sequences, we prove that the set of admissible symbol sequences forms a Cantor set. (c) 2000 American Institute of Physics.

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“…As a model problem, we used the free-fall three-body problem, since we knew the structure of the phase space (Tanikawa et al 1995;Tanikawa, Umehara 1998). We integrated orbits up to the third triple-encounter using the respective criteria, saw the different results, and looked for the best criterion.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…There are various ways of discretization in the three-body problem. One counts the number of binary collisions (Tanikawa et al 1995;Zare, Chesley 1998;Tanikawa, Mikkola 2000) or counts the number of triple encounters (Boyd, McMillan 1992, 1993Tanikawa, Umehara 1998). Thus, there is an increasing demand to accurately define the state of a triple encounter.…”

Section: Introductionmentioning

confidence: 99%