Dynamical behaviour of Lagrangian systems on Finsler manifolds.

Details Dynamical behaviour of Lagrangian systems on Finsler manifolds. Dynamical behaviour of Lagrangian systems on Finsler manifolds.

Jun 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phrve..55.6448d&link_type=abstract

Physical Review E, Vol. 55, No. 6, p. 6448 - 6458

Mathematics

Logic

6

Cosmological Models: Bianchi Models

Scientific paper

The authors develop a theoretical framework devoted to a geometrical description of the behaviour of dynamical systems and their chaotic properties. The underground manifold is a Finsler space whose features permit the description of a wide class of dynamical systems such as those with potentials depending on the time and velocities for which the Riemannian approach is unsuitable. Another appealing feature of this more general setting relies on its very origin: Finsler spaces arise in a direct way on imposing the invariance for time reparametrization to a standard variational problem. In particular, the authors present the following: (i) an exhaustive description and numerical results for a resonant oscillator with a time-dependent potential, (ii) an exact description (without any approximation) of the dynamics of Bianchi type-IX cosmological models, and (iii) a geometrical description of the restricted three-body problem whose effective potential depends linearly on the velocities.

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