Ergodic Theory and Dynamical Systems

Research Article

The C1 Closing Lemma, including Hamiltonians

Charles C. Pugha1 and Clark Robinsona2

a1 University of California, Berkeley, California 94720, USA

a2 Northwestern University, Evanston, Illinois 60201, USA

Abstract

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)