Cohomological equation and local conjugacy class of Diophantine interval exchange maps

TL;DR

This paper extends results on cohomological equations and local conjugacy classes of Diophantine interval exchange maps, addressing a question about their codimension for specific self-similar cases.

Contribution

It advances understanding of the local conjugacy classes of interval exchange maps of restricted Roth type, especially for self-similar examples like Eierlegende Wollmilchsau and Ornithorynque.

Findings

Determined the codimension of local conjugacy classes for specific self-similar maps.

Extended previous results of Marmi--Moussa--Yoccoz to new classes of interval exchange maps.

Provided answers to Krikorian's question on codimension in these contexts.

Abstract

We extend some results of Marmi--Moussa--Yoccoz on the cohomological equations and local conjugacy classes of interval exchange maps of restricted Roth type. In particular, we answer a question of Krikorian about the codimension of the local conjugacy class of self-similar interval exchange maps associated to the Eierlegende Wollmilchsau and the Ornithorynque.