If a vector-function X(t,x) is \,2\omega-periodic with respect to \,t, then \,F(-\omega,x) is the in-period \,[-\omega;\omega] transformation (Poincaré map) of the differential system \dot x=X(t,x).
For the Reflecting Function \,F(t,x) of the system \dot x=X(t,x) the basic relation .