Abstract:
We consider two mass points of masses m 1=m 2= moving under Newton's law of gravitational attraction in a collision elliptic orbit while their centre of mass is at rest. A third mass point of mass m 3≈ 0, moves on the straight line L, perpendicular to the line of motion of the first two mass points and passing through their centre of mass. Since m 3≈ 0, the motion of the masses m 1 and m 2 is not affected by the third mass, and from the symmetry of the motion it is clear that m 3 will remain on the line L. So the three masses form an isosceles triangle whose size changes with the time. The elliptic collision restricted isosceles three-body problem consists in describing the motion of m 3.
In this paper we show the existence of a Bernoulli shift as a subsystem of the Poincaré map defined near a loop formed by two heteroclinic solutions associated with two periodic orbits at infinity. Symbolic dynamics techniques are used to show the existence of a large class of different motions for the infinitesimal body.
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Accepted July 6, 2000¶Published online February 14, 2001
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Alvarez, M., Llibre, J. Heteroclinic Orbits and Bernoulli Shift¶for the Elliptic Collision Restricted¶Three-Body Problem. Arch. Rational Mech. Anal. 156, 317–357 (2001). https://doi.org/10.1007/s002050100116
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DOI: https://doi.org/10.1007/s002050100116