Mironenko reflecting function explained
In applied mathematics, the reflecting function
of a differential system
connects the past state
of the system with the future state
of the system by the formula
The concept of the reflecting function was introduced by
Uladzimir Ivanavich Mironenka.
Definition
with the general solution
in
Cauchy form, the Reflecting Function of the system is defined by the formula
Application
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
Ft+FxX+X(-t,F)=0, F(0,x)=x.
is holding.
Therefore we have an opportunity sometimes to find Poincaré map of the non-integrable in quadrature systems even in elementary functions.
Literature
External links
