Abstract
We obtain the Lax equations associated with a dynamical system endowed with a bilagrangian connection and a closed two-form Ω parallel along the dynamical field Γ. The case of Lagrangian dynamical systems is analysed and the nonnoether constants of motion found by Hojman and Harleston are recovered as being associated to a reduced Lax equation. Completely integrable dynamical systems are also shown to be a particular case of these systems.
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Cariñena, J.F., Ibort, L.A. Bilagrangian connections and the reduction of Lax equations. Lett Math Phys 8, 359–365 (1984). https://doi.org/10.1007/BF00418110
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DOI: https://doi.org/10.1007/BF00418110