Hölder regularity of the solutions of the cohomological equation for Roth type interval exchange maps

2014/07/07 by Stefano Marmi, Marmi, Stefano, Jean-Christophe Yoccoz +1
Mathematics · Medicine · Physics and Astronomy · #11J70 #37J40 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Epidemiology and Ecology Models #Primary: 37C15 #Quantum chaos and dynamical systems #Secondary: 37E05 #math.DS #msc:11J70 #msc:37C15 #msc:37E05 #msc:37J40

paper · pdf · doi:10.48550/arxiv.1407.1776

22 pages

arxiv created 2014/07/07 · openalex publication_date 2014/07/07 · arxiv updated 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Deviation for interval exchange transformations

Related

• On the cohomological equation for interval exchange maps
• The cohomological equation for Roth type interval exchange maps
• Cohomological equation and local conjugacy class of Diophantine interval exchange maps
• Linearization of generalized interval exchange maps
• Cohomological equations for linear involutions