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...
| Autores: | , |
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| 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 |
| 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. |
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