Hölder Regularity of the Solutions of the Cohomological Equation for Roth Type Interval Exchange Maps

Abstract

ABSTRACT. We prove that the solutions of the cohomological equation for Roth type interval exchange maps are Hölder continuous provided that the datum is of class C r with r > 1 and belongs to a finite-codimension linear subspace.

Ruelle spectrum of linear pseudo-Anosov maps

“…Moreover, the k-th derivative of the solution of the coboundary equation is automatically Hölder continuous. This corresponds in our context respectively to the results of [For07] and [MY16].…”

“…Hence, the solution F to the cohomological equation is automatically Hölder continuous, without any further assumption. This corresponds in a different setting to the main result of [MY16].…”

Cohomological equation and local conjugacy class of Diophantine interval exchange maps

“…Theorem A generalizes the results of [9] which were proved for i.e.t. 's of Roth type, that is, for i.e.t.…”

“…'s) which generalize the class of Roth type i.e.t. 's, introduced by Marmi, Moussa and Yoccoz in [9], and we extend the results on cohomological equations of [9] and the linearization results of [10] to these new classes, for sufficiently small values of the exponent η 0. The classes DC(η, θ, σ) depend on parameters η 0, θ > 0 and σ > 0 such that η is the analogous of the Diophantine exponent of circle rotations (in particular η = 0 for Roth type i.e.t.…”

On the Hausdorff dimension of minimal interval exchange transformations with flips

“…On the other hand, every path which is a concatenation of at least complete paths is positive. The proof repeats literally the one for IETs (see [, Section 1.2.3] for technical details).…”