Nonstandard Separability on the Minkowski Plane

Abstract

We present examples of nonstandard separation of the natural Hamilton-Jacobi equation on the Minkowski plane M 2 . By "nonstandard" we refer to the cases in which the form of the metric, when expressed in separating coordinates, does not have the usual Liouville structure. There are two possibilities: the "complex-Liouville" (or "harmonic") case and the "linear/null" (or "Jordan block") case. By means of explicit examples, we show that, in all cases, a suitable glueing of coordinate patches of the different structures allows us to separate natural systems with indefinite kinetic energy all over M 2 .

Periodic orbits associated to Hamiltonian functions of degree four

“…On the other hand, the natural systems with indefinite kinetic energy (the "cosmological Hamiltonian" in the language of our work) have recently been investigated by [24] and [25].…”