Liapunov exponents of simple smooth flows

Abstract

An attempt is made to introduce the notion of a ‘‘simple dynamical system’’ as one, where Liapunov exponents may be obtained by purely algebraic methods, specifically by exploiting the Lie algebra relations between vector fields. Thus, in a simple system, one need not solve the dynamical equations but is often faced with an equally difficult task of unravelling the algebraic structure. The theory is presented within the framework of differential geometry. Several examples illustrate the usefulness of the proposed concept.