Periodic and Chaotic Trajectories of the Second Species for the n-Centre Problem
Abstract
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’.
- Publication:
-
Celestial Mechanics and Dynamical Astronomy
- Pub Date:
- July 2000
- DOI:
- 10.1023/A:1008393706818
- Bibcode:
- 2000CeMDA..77...49B
- Keywords:
-
- N-CENTRE PROBLEM;
- 3-BODY PROBLEM;
- SECOND SPECIES ORBITS;
- COLLISIONS;
- REGULARISATION