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.
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Last modified: April 08 2016 - 20:30:35