Description cohérente en géométrie Riemannienne de l'ordre hamiltonien et du chaos avec métrique de Jacobi
| Autor: | Matteo Gori, Marco Pettini, Loris Di Cairano |
|---|---|
| Přispěvatelé: | Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), CPT - E7 Systèmes dynamiques : théories et applications, Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Integrable system
Geodesic General Physics and Astronomy FOS: Physical sciences 01 natural sciences Instability 010305 fluids & plasmas Newtonian dynamics symbols.namesake 0103 physical sciences 010306 general physics Condensed Matter - Statistical Mechanics Mathematical Physics Mathematics Differential Geometry Statistical Mechanics (cond-mat.stat-mech) Applied Mathematics Statistical and Nonlinear Physics Nonlinear Sciences - Chaotic Dynamics 16. Peace & justice Classical mechanics Differential geometry [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD] symbols Hamiltonian Chaos Configuration space Chaotic Dynamics (nlin.CD) Hamiltonian (quantum mechanics) |
| Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2019, 29 (12), pp.123134. ⟨10.1063/1.5119797⟩ Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019, 29 (12), pp.123134. ⟨10.1063/1.5119797⟩ |
| ISSN: | 1054-1500 |
| Popis: | International audience; 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 non-affine parametrization of the arc length with physical time. To 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 artefacts. |
| Databáze: | OpenAIRE |
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