Mironenko reflecting function

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The reflecting function of a dynamical system connects the past state of it with the future state of it by the formula The concept of the reflecting function was introduсed by Uladzimir Ivanavich Mironenka.


For the differential system with the general solution in Cauchy form Reflecting Function is defined by formula


If a vector-function is -periodic with respect to , then is the in-period transformation (Poincaré map) of the differential system Therefore the knowledge of the Reflecting Function give us the opportunity to find out the initial dates of periodic solutions of the differential system and investigate the stability of those solutions.

For the Reflecting Function of the system the basic relation

is holding.

Therefore we have an opportunity sometimes to find Poincaré map of the non-integrable in quadrature systems even in elementary functions.


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