Interpolation in dynamic equations on time scales†

Abstract

It is known that small time-gaps of dynamic equations can be filled by families of trajectory segments of ordinary differential equations and thus certain types of dynamic equations, together with the nonautonomous solution flows they generate, extend to differential equations defined on the entire real line. This phenomenon, for small and large time-gaps alike, is discussed in what we think to be the proper framework for it—Hermite interpolation in groups of diffeomorphisms.