Multiple conventions have been adopted for denoting Interval Exchange Transformations (IETs). The "non-labeled" convention was the original, while the "labeled" convention has proven convenient when investigating Flat Surfaces as described by IETs. We establish the relationship between Extended Rauzy Classes, an equiva…
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Let be a non-degenerate permutation on at least symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation is path-connected.
The paper calculates Hausdorff dimensions for Teichmüller geodesics and related sets.
problem Calculating Hausdorff dimensions for specific sets of Teichmüller geodesics.
method Analyzing flat surfaces and Teichmüller geodesics to determine dimensions.
result Hausdorff dimensions for specific sets of Teichmüller geodesics are strictly less than 1 and bounded above by 1/2.