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Infinitesimal symmetries in Contact Hamiltonian systems

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arxiv 1909.07892 v2 pith:RZ23H5S2 submitted 2019-09-17 math-ph math.DGmath.DSmath.MPmath.SG

Manuel de León , Manuel Lainz Valcázar This is my paper · ORCID
classification math-phmath.DGmath.DSmath.MPmath.SG
keywords contactinfinitesimalquantitiessymmetriessystemsconservedcorrespondinglagrangian
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In this paper, we extend the well-known Noether theorem for Lagrangian systems to contact Lagrangian systems. We introduce a classification of infinitesimal symmetries and obtain the corresponding dissipated quantities. We notice that in contact dynamics, the existence of infinitesimal symmetries does not produce conserved quantities, but functions that dissipate at the same rate than the energy; so, the corresponding quotients are true conserved quantities.

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  1. Contact line bundles, foliations, and integrability

    math.SG 2025-02 conditional novelty 6.0 of 10

    A line-bundle approach to contact integrability unifies cooriented and non-cooriented systems and covers dissipative contact Hamiltonians.

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