Instabilities in Hamiltonian systems
In 1964, V. I. Arnol'd proved the existence of nearly-integrable Hamiltonian systems which have global instabilities (global chaotic behaviour). This phenomenon is nowadays termed under the name "Arnol'd diffusion". One of the key ideas that he used is to "travel" along...
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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:2117/106772 |
| Acceso en línea: | https://hdl.handle.net/2117/106772 |
| Access Level: | acceso abierto |
| Palabra clave: | Hamiltonian systems Arnol'd diffusion Melnikov function Near-integrable Hamiltonian system Splitting of separatrices Hamilton, Sistemes de Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | In 1964, V. I. Arnol'd proved the existence of nearly-integrable Hamiltonian systems which have global instabilities (global chaotic behaviour). This phenomenon is nowadays termed under the name "Arnol'd diffusion". One of the key ideas that he used is to "travel" along invariant manifolds of the Hamiltonian system. The purpose of this project is to understand the Arnol'd instability mechanism and study new ones using different invariant objects. |
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