a1 University of California, Berkeley, California 94720, USA
a2 Northwestern University, Evanston, Illinois 60201, USA
An Axiom of Lift for classes of dynamical systems is formulated. It is shown to imply the Closing Lemma. The Lift Axiom is then verified for dynamical systems ranging from C1 diffeomorphisms to C1 Hamiltonian vector fields.
(Received May 22 1981)