Abstract

TORRES DEL CASTILLO, G.F.  and  AZUAJE, R.. Constants of motion associated with canonoid transformations for non-autonomous systems. Rev. mex. fis. [online]. 2022, vol.68, n.2, e020706.  Epub Mar 27, 2023. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.68.020706.

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, $S_{\beta }^{\alpha }$, whose eigenvalues are constants of motion. We prove that if the Nijenhuis torsion tensor of $S_{\beta }^{\alpha }$ is equal to zero then the eigenvalues of $S_{\beta }^{\alpha }$ are in involution, and that these eigenvalues may be in involution even if the Nijenhuis tensor is not zero.

Keywords : Integrable systems; non-autonomous systems; canonoid transformations; Nijenhuis torsion tensor.

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