Reflecting function of a system is a vector-function F(t,x) which give us an opportunity to find out the state x(t) of the system if we know the state x(-t) of the system in a symmetrical moment (-t) of time.

Different systems can have the same reflecting function. If we know reflecting function, then we can write down all differential systems which described the behavior of real systems with the reflecting function. If we know the reflecting function of 2ω-periodic differential system, then F(-ω,x) is the in period [-ω;ω] transformation of the system. Therefore we can find out the initial dates of periodic solutions of the system and the characters of their stability. We can apply the notion of reflecting function to the center-focus problem and boundary problems also.

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