Heteroclinic orbits and bernoulli shift for the elliptic collision restricted three-body problem

Martha Alvarez, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)

Abstract

We consider two mass points of masses m1 = m2 = 1/2 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 m3 ≈ 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 m3 ≈ 0, the motion of the masses m1 and m2 is not affected by the third mass, and from the symmetry of the motion it is clear that m3 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 m3. 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.
Original languageEnglish
Pages (from-to)317-357
JournalArchive for Rational Mechanics and Analysis
Volume156
DOIs
Publication statusPublished - 5 Mar 2001

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