CHAOS AND TIME-COORDINATE

A time parametrization, s, called Maupertuis time, is defined. Accordi ng to the generalized Maupertuis principle (which is actually due to E uler, Lagrange and Jacobi dynamics) can be reduced to the problem of g eodesics on a space with the Jacobi metric. Maupertuis time s is a nat ural parameter along these geodesics. It is equivalent to the Hamilton ian constraint H = 0. Relationships of Maupertuis time with other time parametrizations used in general relativity (cosmological time, Misne r time, Chitre-Misner time, curvature time and superspace time) are in vestigated. In the Bianchi IX Mixmaster world model, the Maupertuis cl ock counts the Kasner epochs. The physical meaning of Maupertius time, as a chaos indicator, is discussed. Copyright (C) 1996 Elsevier Scien ce Ltd.