Abstract
We study a class of nonuniformly expanding interval maps with a neutral fixed point at 0, a class that includes Manneville–Pomeau maps. We prove that the set of points whose forward orbits miss an interval with left endpoint 0 is strong winning for Schmidt’s game. Strong winning sets are dense, have full Hausdorff dimension, and satisfy a countable intersection property. Similar results were known for certain expanding maps, but these did not address the nonuniformly expanding case. Our analysis is complicated by the presence of infinite distortion and unbounded geometry.
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