N-BODY CHOREOGRAPHIES WITH A REFLECTIONAL SYMMETRY - COMPUTER ASSISTED EXISTENCE PROOFS

TOMASZ KAPELA
2005 EQUADIFF 2003  
We proof the existence of symmetric choreographies -solutions of the planar Nbody problem on which all bodies travel on the same curve. We describe general method of computer assisted proofs using reflectional symmetry of the orbit to isolate a solution. Using this method we proved, as an example, the existence of many choreographies of 4 and 5 bodies.
doi:10.1142/9789812702067_0165 fatcat:szi5nl3emzd6th5yub74i5r2ma