Chaos and time coordinate

A time parametrization, s, called Maupertuis time, is defined. According to the generalized Maupertuis principle (which is actually due to Euler, Lagrange and Jacobi dynamics) can be reduced to the problem of geodesies on a space with the Jacobi metric. Maupertuis time s is a natural parameter along these geodesies. It is equivalent to the Hamiltonian constraint = 0. Relationships of Maupertuis time with other time parametrizations used in general relativity (cosmological time, Misner time, Chitre-Misner time, curvature time and superspace time) are investigated. In the Bianchi IX Mixmaster world model, the Maupertuis clock counts the Kasner epochs. The physical meaning of Maupertuis time, as a chaos indicator, is discussed.