By generalising earlier results, we prove that whenever a Lagrangian dynamical system can be associated with a (1,1)-type tensor field which is left invariant by the dynamics, satisfies the Nijenhuis condition and is compatible with the tangent bundle structure, the system necessarily decomposes into a collection of lower-dimensional mutually non-interacting Lagrangian subsystems.
A separability theorem for dynamical systems admitting alternative Lagrangian descriptions
FERRARIO, Carlo;LO VECCHIO, Guido;MORANDI, Giuseppe;
1987
Abstract
By generalising earlier results, we prove that whenever a Lagrangian dynamical system can be associated with a (1,1)-type tensor field which is left invariant by the dynamics, satisfies the Nijenhuis condition and is compatible with the tangent bundle structure, the system necessarily decomposes into a collection of lower-dimensional mutually non-interacting Lagrangian subsystems.File in questo prodotto:
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