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Schmidt's Game and Nonuniformly Expanding Interval Maps
[Submitted on 27 Nov 2019 (v1), last revised 15 Jun 2026 (this v · 2026-06-17 · via math updates on arXiv.org

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Abstract:We study Manneville-Pomeau maps on the unit interval and 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.

Submission history

From: Jason Duvall [view email]
[v1] Wed, 27 Nov 2019 08:02:44 UTC (211 KB)
[v2] Mon, 15 Jun 2026 21:03:55 UTC (355 KB)

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