General disagreement between the Geometrical Description of Dynamical In-stability -using non affine parameterizations- and traditional Tangent Dynamics
| dc.creator | Cuervo-Reyes, Eduardo | |
| dc.date | 2008-07-08 | |
| dc.date.accessioned | 2026-07-07T09:49:00Z | |
| dc.date.available | 2026-07-07T09:49:00Z | |
| dc.description | In this paper, the general disagreement of the geometrical lyapunov exponent with lyapunov exponent from tangent dynamics is addressed. It is shown in a quite general way that the vector field of geodesic spread $ξ^k_G$ is not equivalent to the tangent dynamics vector $ξ^k_T$ if the parameterization is not affine and that results regarding dynamical stability obtained in the geometrical framework can differ qualitatively from those in the tangent dynamics. It is also proved in a general way that in the case of Jacobi metric -frequently used non affine parameterization-, $ξ^k_G$ satisfies differential equations which differ from the equations of the tangent dynamics in terms that produce parametric resonance, therefore, positive exponents for systems in stable regimes. | |
| dc.description | 8 pages in preprint format or 4 pages in pre format. 0 figures | |
| dc.identifier | https://arxiv.org/abs/0807.1156 | |
| dc.identifier | http://arxiv.org/abs/0807.1156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164427 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 37D99; 37J99 | |
| dc.title | General disagreement between the Geometrical Description of Dynamical In-stability -using non affine parameterizations- and traditional Tangent Dynamics | |
| dc.type | text |