Periodic and Chaotic Trajectories of the Second Species for the n-Centre Problem

Details Periodic and Chaotic Trajectories of the Second Species for the n-Centre Problem Periodic and Chaotic Trajectories of the Second Species for the n-Centre Problem

Jul 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000cemda..77...49b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 77, Issue 1, p. 49-75 (2000).

Astronomy and Astrophysics

Astronomy

6

N-Centre Problem, 3-Body Problem, Second Species Orbits, Collisions, Regularisation

Scientific paper

For the n-centre problem of one particle moving in the potential of attracting centres of small mass fixed in an arbitrary smooth potential and magnetic field, we prove the existence of periodic and chaotic trajectories shadowing sequences of collision orbits. In particular, we obtain large subshifts of solutions of this type for the circular restricted 3-body problem of celestial mechanics. Poincaré had conjectured existence of the periodic ones and given them the name ‘second species solutions’.

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