a1 Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA and Mathematics Institute, University of Warwick, Coventry CV47AL, England
We develop simple topological criteria for the existence of periodic orbits in maps of the annulus. These are applied to one-parameter families of dissipative twist maps of the annulus and their attractors. It follows that many of the motions found by variational methods in area preserving twist maps also occur in the dissipative case.
(Received November 15 1985)
(Revised March 07 1986)