Chaotic dynamics of the Kepler problem with variable gravitational coefficient
On this work we prove the presence of chaotic dynamics for the classical two-body Kepler problem with a time-periodic variable gravitational coefficient using two different methods, the stretching along the path (SAP) technique and the Melnikov method. For the SAP method, a piecewise periodic consta...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/106631 |
| Acceso en línea: | https://hdl.handle.net/2117/106631 |
| Access Level: | acceso abierto |
| Palabra clave: | Differentiable dynamical systems Kepler Problem Chaos Melnikov method Periodic solutions Stretching along the path Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | On this work we prove the presence of chaotic dynamics for the classical two-body Kepler problem with a time-periodic variable gravitational coefficient using two different methods, the stretching along the path (SAP) technique and the Melnikov method. For the SAP method, a piecewise periodic constant function is taken as the time-periodic coefficient, and the chaotic dynamics are obtained for small values of angular momentum or large periods. For the Melnikov method, a sinusoidal perturbation function is taken as the time-periodic coefficient. To guarantee chaotic dynamics big values of angular momentum or small periods of the function are necessary. The classical Melnikov method could not be applied, as the critical point of the system was parabolic, not hyperbolic. Hence, some modifications to the method have been necessary. |
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