6 citations · 14 across the 7 of their papers we have counts for
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Decoding Rauzy Induction: An Effective Answer to Bufetov's Question
Jon Fickenscher
A typical interval exchange transformation has an infinite sequence of matrices associated to it by successive iterations of Rauzy induction. In 2010, W. A. Veech answered a questi…
The number of ergodic measures for transitive subshifts under the regular bispecial condition
Michael Damron, Jon Fickenscher
If is a finite set (alphabet), the shift dynamical system consists of the space of sequences with entries in , along with the…
On the number of ergodic measures for minimal shifts with eventually constant complexity growth
Michael Damron, Jon Fickenscher
In 1985, Boshernitzan showed that a minimal (sub)shift satisfying a linear block growth condition must have a bounded number of ergodic probability measures. Recently, this bound w…
Decoding Rauzy Induction: An Answer to Bufetov's General Question
Jon Fickenscher
Given a typical interval exchange transformation, we may naturally associate to it an infinite sequence of matrices through Rauzy induction. These matrices encode visitations of th…
Labeled and Non-labeled Extended Rauzy Classes
Jon Fickenscher
Multiple conventions have been adopted for denoting Interval Exchange Transformations (IETs). The "non-labeled" convention was the original, while the "labeled" convention has prov…
Topological mixing for some residual sets of interval exchange transformations
Jon Chaika, Jon Fickenscher
We show that a residual set of non-degenerate IETs on more than 3 letters is topologically mixing. This shows that there exists a uniquely ergodic topologically mixing IET. This is…
A Combinatorial Proof of the Kontsevich-Zorich-Boissy Classification of Rauzy Classes
Jon Fickenscher
Rauzy Classes and Extended Rauzy Classes are equivalence classes of permutations that arise when studying Interval Exchange Transformations. In 2003, Kontsevich and Zorich classifi…
Self-inverses in Rauzy Classes
Jonathan Fickenscher
Thanks to works by M. Kontsevich and A. Zorich followed by C. Boissy, we have a classification of all Rauzy Classes of any given genus. It follows from these works that Rauzy Class…