On the Complexity of the Anisotropic Kepler Problem and the Planar Isosceles Three Body Problem

Hava T. Siegelmann and Jeremy Schiff

We show how to associate a computation to certain 2 degree of freedom hamiltonian systems, and use this to discuss the level of complexity of certain problems in the dynamics of these systems. A type of Turing machine over the reals can be identified, embedded in these systems.

Publication information: This paper was submitted to Complex Systems. We got an encouraging referee report (the referee identified himself as Cris Moore) and a conditional acceptance provided we dealt with the points the referee raised. Unfortunately Hava left Bar-Ilan and we never got around to it.