Nonintegrability of the Armbruster-Guckenheimer-Kim Quartic Hamiltonian Through Morales-Ramis Theory

We show the nonintegrability of the three-parameter Armburster--Guckenheimer--Kim quartic Hamiltonian using Morales--Ramis theory, with the exception of the three already known integrable cases. We use Poincaré sections to illustrate the breakdown of regular motion for some parameter values.

Autores:
Acosta-Humánez, P.
Alvarez-Ramírez, M.
Stuchi, T.J.
Tipo de recurso:
Fecha de publicación:
2018
Institución:
Universidad Simón Bolívar
Repositorio:
Repositorio Digital USB
Idioma:
eng
OAI Identifier:
oai:bonga.unisimon.edu.co:20.500.12442/1725
Acceso en línea:
http://hdl.handle.net/20.500.12442/1725
Palabra clave:
Hamiltonian
Integrability of dynamical systems
Diferential Galois theory
Legendre equation
Schrodinger equation
Rights
License
Licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional
Description
Summary:We show the nonintegrability of the three-parameter Armburster--Guckenheimer--Kim quartic Hamiltonian using Morales--Ramis theory, with the exception of the three already known integrable cases. We use Poincaré sections to illustrate the breakdown of regular motion for some parameter values.