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

By Stefano Marmi, J. Yoccoz. 2004

147 citations recorded by the source corpus.

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 $${C^r}$$Cr with $${r > 1}$$r>1 and belongs to a finite-codimension linear subspace.

Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b3c243296b52f65f3584cde7c916020091c955dc

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In Computer Networks and Communications

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Introduction to Teichm\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (2013, methodology): “sed on a reduction to the cohomological equation INTRODUCTION TO TEICHMULLER DYNAMICS 63 for interval exchange transformations can be derived from the results of S. Marmi, P. Moussa and J.-C. Yoccoz [53]. Recently, A. Bufetov [14] has developed the methods of Forni’s paper [29] and proved rened devi”
Ergodic Theory of Interval Exchange Maps (2006, methodology): “Besides the original papers mentioned previously, we have also benefited from the presentations of Marmi, Moussa, Yoccoz [16,24].”
Chapter 8 - On the Lyapunov Exponents of the Kontsevich–Zorich Cocycle (2006, unknown): “The spectral gap property of the cocycle also plays an important role in recent results of Marmi, Moussa and Yoccoz [27,28] on the cohomological equation for generic i.e.t.’s, which improve on previous work of the author [19].”
Non-ergodic Z-periodic billiards and infinite translation surfaces (2011, background): “Remark that since (φt )t∈R has no vertical saddle connections, T satis es the Keane's condition and in particular it is minimal (see for example [36] or [53]).”
Limit theorems for translation flows (2008, methodology): “For a different presentation of the Rauzy-Veech formalism, see Marmi-Moussa-Yoccoz [32].”
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture (2005, methodology): “Let us point out that it is now possible to treat the case of interval exchange transformations in a very elegant way, using the results of Marmi‐Moussa‐Yoccoz [ MMY ].”