Celestial mechanics: Topology of the threebody problem. Volume 5. Parts 1 & 2
Abstract
The book is a detailed review of the mathematical research and methods developed in order to find qualitative and topological solutions to the threebody problem. After examining the problem of the existence of solutions to the differential equations, including conditions for collisions, the WeierstrassSundman theorem, behavior at infinity, and the problem of captures, the discussion covers topological theory as it applies to the threebody problem. Topics investigated include Poincare's theory of characteristics, characteristics in higherdimensional spaces, geodesics on surface of negative and positive curvature, geodesics on a torus, Fuchsian groups, variational principles, Ndimensional analysis situs, functional topology, surface transformations, the last geometric theorem of Poincare and its application to dynamical systems, recurrent motions and point groups, Poincare's recurrence theorem and Khinchin's sharpening of it, ergodic theorems of Birkhoff and von Neumann, and the question of Liapunov stability and almost periodic motions.
 Publication:

Japan Society of Promotion Science
 Pub Date:
 1976
 Bibcode:
 1976JSPS..........H
 Keywords:

 Astrodynamics;
 Celestial Mechanics;
 Orbit Calculation;
 Three Body Problem;
 Topology;
 Collision Parameters;
 Dynamic Stability;
 Geodesic Lines;
 Periodic Functions;
 Poincare Problem;
 Astronomy