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Geometrical Dissipation for Dynamical Systems

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Abstract

On a Riemannian manifold (M, g) we consider the k + 1 functions F 1, . . . , F k , G and construct the vector fields that conserve F 1, . . . , F k and dissipate G with a prescribed rate. We study the geometry of these vector fields and prove that they are of gradient type on regular leaves corresponding to F 1, . . . , F k . By using these constructions we show that the cubic Morrison dissipation and the Landau-Lifschitz equation can be formulated in a unitary form.

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Correspondence to Petre Birtea.

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Communicated by G. Gallavotti

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Birtea, P., Comănescu, D. Geometrical Dissipation for Dynamical Systems. Commun. Math. Phys. 316, 375–394 (2012). https://doi.org/10.1007/s00220-012-1589-6

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  • DOI: https://doi.org/10.1007/s00220-012-1589-6

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