# Recurrence on infinite cyclic coverings

• Albert Fathi, ENS Lyon
• Wednesday 08 July 2015, 16:15-17:15
• MR4.

If h is a homeomorphism of the compact space Z which is homotopic to the identity, and \tilde{Z}->Z is an infinite cyclic covering, then we can lift h to a homeomorphism \tilde{h} of \tilde{Z}.

We will compare the recurrence properties of h and \tilde{h}. Our main result is is if the chain recurrent set of \tilde{h} is empty, then h has a non-trivial compact attractor. The generalizes work of Franks on the annulus, and should be compared with the work of Atkinson in the measurable category. It can be considered as a weak generalization of the Poincare-Birkhoff theorem.

This talk is part of the Differential Geometry and Topology Seminar series.