Schmidt's Game and Nonuniformly Expanding Interval Maps
Dynamical Systems
2020-10-28 v1
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.
Cite
@article{arxiv.1911.12004,
title = {Schmidt's Game and Nonuniformly Expanding Interval Maps},
author = {Jason Duvall},
journal= {arXiv preprint arXiv:1911.12004},
year = {2020}
}
Comments
16 pages, 6 figures. Submitted to Nonlinearity