Trivial Flow Immersion in the Extremals Field

Mikhail R. Petrichenko \& Dmitry W. Serow

St.\,Petersburg State Polytechnic University, Russia

Is there an immersion of characteristics of the system $\dot{x}=f(x)$ into the extremals flow? For arbitrary differentiations ring condition immersion into the extremals flow is a Liouville's theorem paraphrase about the invariance measures in the phase space.