LIAPUNOV EXPONENTS OF SIMPLE SMOOTH FLOWS

An attempt is made to introduce the notion of a ''simple dynamical sys tem'' as one, where Liapunov exponents may be obtained by purely algeb raic methods, specifically by exploiting the Lie algebra relations bet ween vector fields. Thus, in a simple system, one need not solve the d ynamical equations but is often faced with an equally difficult task o f unravelling the algebraic structure. The theory is presented within the framework of differential geometry. Several examples illustrate th e usefulness of the proposed concept.