The set of non-uniquely ergodic d-IETs has Hausdorff codimension 1/2
Jon Chaika, Howard Masur
TL;DR
This paper determines the Hausdorff dimension of the set of non-uniquely ergodic d-interval exchange transformations (d-IETs), showing it has dimension d-3/2 for d>4, extending previous results for lower dimensions.
Contribution
It establishes the Hausdorff dimension of the set of not uniquely ergodic d-IETs for all d>4, filling a gap in the understanding of their geometric complexity.
Findings
Hausdorff dimension of non-uniquely ergodic d-IETs is d-3/2 for d>4
Confirmed previous results for d=2,3,4
Extended the dimension analysis to higher dimensions
Abstract
We show that the set of not uniquely ergodic d-IETs has Hausdorff dimension d-3/2 (in the (d-1)-dimension space of d-IETs) for d>4. For d=4 this was shown by Athreya-Chaika and for d=2,3 the set is known to have dimension d-2.
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