Constants of motion associated with canonoid transformations for non-autonomous systems
DOI:
https://doi.org/10.31349/RevMexFis.68.020706Keywords:
Integrable systems, non-autonomous systems, canonoid transformations, Nijenhuis torsion tensorAbstract
We consider non-autonomous systems of ordinary differential equations that can be expressed in Hamiltonian form in terms of two different coordinate systems, not related by a canonical transformation. We show that the relationship between these coordinate systems leads to a, possibly time-dependent, tensor field, $S^{\alpha}_{\beta}$, whose eigenvalues are constants of motion. We prove that if the Nijenhuis torsion tensor of $S^{\alpha}_{\beta}$ is equal to zero then the eigenvalues of $S^{\alpha}_{\beta}$ are in involution, and that these eigenvalues may be in involution even if the Nijenhuis tensor is not zero.
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Copyright (c) 2022 Gerardo Francisco Torres del Castillo, Rafael Azuaje
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