Denis Gaidashev, Existence of topological attractors for dissipative maps of the annulus

Abstract:   Recently, E. Pujals asked a question, whether, when considering small 2D perturbations of critical circle maps, one would observe critical invariant circles: that is, topological circles  on which the dynamics is topologically, but not smoothly, conjugate to an irrational rotation.

We develop a renormalization theory for a class of dissipative perturbations of critical circle maps and use it to prove a version of Pujals' conjectures.

This is a joint work with M. Yampolsky (Univ. of Toronto)