Physics

Prof. Govind S. Krishnaswami
Chennai Mathematical Institute, Chennai

Abstract : The classical three body problem has been a rich source of phenomena
and a context for developing techniques. Euler and Lagrange found
periodic solutions while Poincare discovered chaos in this problem.
Its study catalyzed the development of perturbation theory and
canonical transformations and has shed light on the nature of
singularities. After surveying some highlights, we describe new
results on a simpler variant: the three rotor problem. We find
analogues of Euler-Lagrange periodic orbits and choreographies. Energy
in units of a coupling serves as a control parameter. Integrability at
very low energies gives way to a rather marked transition to chaos at
E = 4 followed by a regime of global chaos and a gradual return to
regularity as E diverges. We discuss three signatures of this
transition to chaos: a change in the character of Poincare sections, a
change in sign of a curvature and an accumulation of `phase
transitions’. This talk is based on joint work with Himalaya Senapati.