Complete and incomplete additive doubling variables in linear systems with constant coefficients


Differential equations and their systems, not associated with any of the variational problems have been put forward to transform up to Hamiltonian form and immerse their solutions into a bundle of extremities. For small momenta the doubled system of the equations corresponds closely with the original one but for the equations in variations.

Totally or partly additive doubled system of linear equations with constant coefficients has a Hamilton structure. For Jordan cells in the matrix of coefficients of the system complete and partial doubling correspond closely, with an accuracy up to a shift operator, which is representable in the basis of its own and associated vectors of a nilpotent matrix.