The integrability of the Nose-Hoover equation

In this work we consider the Nos'e-Hoover equation for a one dimensional oscillator x˙ = -y - xz, y˙ = x, z˙ = α(x2 - 1). It models the interaction of a particle with a heat-bath. We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its o...

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Detalles Bibliográficos
Autores: Mahdi, Adam, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150423
Acceso en línea:https://ddd.uab.cat/record/150423
https://dx.doi.org/urn:doi:10.1016/j.geomphys.2011.02.018
Access Level:acceso abierto
Palabra clave:Nosé-Hoover equation
Darboux integrability
Invariant algebraic surfaces
Descripción
Sumario:In this work we consider the Nos'e-Hoover equation for a one dimensional oscillator x˙ = -y - xz, y˙ = x, z˙ = α(x2 - 1). It models the interaction of a particle with a heat-bath. We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its orbits by studying the integrability problem. We prove that α = 0 is the only value of the parameter for which the system is integrable, and in this case we provide an explicit expression for its first integrals.