Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivska Street, 01601 Kyiv-4, UKRAINE
e-mail: boyko@imath.kiev.ua
e-mail: rop@imath.kiev.ua
http://www.imath.kiev.ua/~boyko/

Differential Invariants and Integration of Riccati-Type Systems

Abstract:
A new tool to construction of differential invariants for a one-parameter group of local transformations in the space of n independent and m dependent  variables is proposed. It is proved that if its universal invariant is known then a complete set of
functionally independent differential invariants can be constructed via one quadrature and differentiations. Relation of first-order differential invariants to systems of Riccati-type systems is analysed.