- Definition
- Application
- Literature
- External links
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
For the differential system 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
is holding.
Therefore we have an opportunity sometimes to find Poincaré map of the non-integrable in quadrature systems even in elementary functions.
Literature
- Мироненко В. И. Отражающая функция и периодические решения дифференциальных уравнений. — Минск, Университетское, 1986. — 76 с.
- Мироненко В. И. Отражающая функция и исследование многомерных дифференциальных систем. — Гомель: Мин. образов. РБ, ГГУ им. Ф. Скорины, 2004. — 196 с.
External links
- The Reflecting Function Site
- How to construct equivalent differential systems
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