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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Detalles Bibliográficos
Autor: Granell i Yuste, Francesc
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
Descripción
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.