A remark on Liouville’s formula on small time scales ✩

We present a new proof of the Liouville formula for a d-dimensional linear dynamic system xΔ = A(t)x on a time scale T, where T is in a sense small. Our proof demonstrates that Liouville’s formula on small time scales is a direct consequence of its well-known counterpart for ordinary differential equations.  2004 Elsevier Inc. All rights reserved.