2 papers
math.DS2025
On the Hausdorff Dimension of Measures for a Non-Uniquely Ergodic Family of Interval Exchange Transformations
Aleksei Kobzev
In this paper, based on a construction by J. Fickenscher, we construct a family of non-uniquely ergodic interval exchange transformations on intervals with the maximal possible…
math.DS2025
Existence of a Non-Uniquely Ergodic Interval Exchange Transformation with Flips Possessing Three Invariant Measures
Aleksei Kobzev
We present the first explicit example of an interval exchange transformation with flips (FIET) possessing three distinct invariant ergodic measures. The proof is based on a general…