Invariance of Cones and Wedges under Flows

摘要

A finite dimensional real vector space L and a vector field X:L mapping L satisfying a Lipschitz condition are considered. If W is a closed subset of L, then many applications demand precise information about conditions on the vector field X which assure that the flow associated with it respects the closed set W. For u: 0,T mapping L is an integral curve of the differential equation u(t) = X(u(t)), u(0) = uo with uo a member of W, u's continuing membership of W is discussed.