Dynamical Systems Seminar

Schmidt's game is a useful tool in the analysis of "exceptional" sets of points with non-dense forward orbits under a given dynamical system. A set that is winning with respect to this game is quite large in a precise sense, and various exceptional sets are known to be winning in the case of a uniformly expanding system. Our result adds the well-studied Manneville-Pomeau interval maps to the collection of systems known to give rise to winning exceptional sets. The key feature of these maps complicating the analysis is nonuniform expansion at a neutral fixed point. In contrast to similar articles, our method of proof does not use symbolic coding or Markov partitions.