Artículo
Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures
Fecha de publicación:
01/2020
Editorial:
American Institute of Physics
Revista:
Journal of Mathematical Physics
ISSN:
0022-2488
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
A Hamilton-Jacobi theory for general dynamical systems, defined on fibered phase spaces, has been recently developed. In this paper, we shall apply such a theory to contact Hamiltonian systems, as those appearing in thermodynamics and on geodesic flows in fluid mechanics. We first study the partial and complete solutions of the Hamilton-Jacobi equation related to these systems. Then, we show that, for a given contact system, the knowledge of what we have called a complete pseudo-isotropic solution ensures the integrability by quadratures of its equations of motion. This extends to contact manifolds a recent result obtained in the context of general symplectic and Poisson manifolds.
Palabras clave:
Hamilton-Jacobi
,
Contact manifolds
,
Integrable systems
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Colecciones
Articulos(CCT - PATAGONIA NORTE)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - PATAGONIA NORTE
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - PATAGONIA NORTE
Citación
Grillo, Sergio Daniel; Padrón, Edith; Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures; American Institute of Physics; Journal of Mathematical Physics; 61; 1; 1-2020; 1-23
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