Coherent Riemannian-geometric description of Hamiltonian order and chaos with Jacobi metric

By identifying Hamiltonian flows with geodesic flows of suitably chosen Riemannian manifolds, it is possible to explain the origin of chaos in classical Newtonian dynamics and to quantify its strength. There are several possibilities to geometrize Newtonian dynamics under the action of conservative...

Full description

Saved in:
Bibliographic Details
Published inChaos (Woodbury, N.Y.) Vol. 29; no. 12; p. 123134
Main Authors Di Cairano, Loris, Gori, Matteo, Pettini, Marco
Format Journal Article
LanguageEnglish
Published United States 01.12.2019
Online AccessGet more information

Cover

More Information
Summary:By identifying Hamiltonian flows with geodesic flows of suitably chosen Riemannian manifolds, it is possible to explain the origin of chaos in classical Newtonian dynamics and to quantify its strength. There are several possibilities to geometrize Newtonian dynamics under the action of conservative potentials and the hitherto investigated ones provide consistent results. However, it has been recently argued that endowing configuration space with the Jacobi metric is inappropriate to consistently describe the stability/instability properties of Newtonian dynamics because of the nonaffine parametrization of the arc-length with physical time. On the contrary, in the present paper, it is shown that there is no such inconsistency and that the observed instabilities in the case of integrable systems using the Jacobi metric are artifacts.
ISSN:1089-7682
DOI:10.1063/1.5119797