# Rigidity of generalized Veech 1969/Sataev 1975 extensions of rotations

@article{Ferenczi2020RigidityOG,
title={Rigidity of generalized Veech 1969/Sataev 1975 extensions of rotations},
author={S{\'e}bastien Ferenczi and Pasacal Hubert},
journal={Journal d'Analyse Math{\'e}matique},
year={2020}
}
• Published 5 October 2020
• Mathematics
• Journal d'Analyse Mathématique
We look at $d$-point extensions of a rotation of angle $\alpha$ with $r$ marked points, generalizing the examples of Veech 1969 and Sataev 1975, together with the square-tiled interval exchange transformations of \cite{fh2}. We study the property of rigidity, in function of the Ostrowski expansions of the marked points by $\alpha$: we prove that $T$ is rigid when $\alpha$ has unbounded partial quotients, and that $T$ is not rigid when the natural coding of the underlying rotation with marked…

## References

SHOWING 1-10 OF 19 REFERENCES

### Rigidity of square-tiled interval exchange transformations

• Mathematics
Journal of Modern Dynamics
• 2019
We look at interval exchange transformations defined as first return maps on the set of diagonals of a flow of direction \begin{document}$\theta$\end{document} on a square-tiled surface: using a

### Trajectories of rotations

• Mathematics
• 1999
= 0; for other points, although the method is easy in principle,technicalities have to be overcome to get manageable formulas. An algorithmis given in [ITO-YAS] and another can be deduced from

### Hausdorff dimension of divergent Teichmüller geodesics

Let g > 1 be given and let k = (k l , ... ,kn ) be an n-tup1e of positive integers whose sum is 4g-4. Denote by Qk the set of all holomorphic quadratic differentials on compact Riemann surfaces of

### Cohomology of step functions under irrational rotations

This paper studies the solvability of the functional equationg(x+θ)=φ(x)g(x), given an irrationalθ and a step functionf mappingR/Z (with Lebesgue measure) to the unit circle. Results are applied to

### Systems of finite rank

0.1. Measure-theoretic dynamical systems 2 0.2. A small glossary of measure-preserving ergodic theory 3 1. Rank one 5 1.1. The lecturer’s nightmare : how to define a rank one system 5 1.2. First

### Boshernitzan's criterion for unique ergodicity of an interval exchange transformation

• W. Veech
• Mathematics
Ergodic Theory and Dynamical Systems
• 1987
Abstract Confirming a conjecture by Boshernitzan, it is proved that if T is a minimal non-uniquely ergodic interval exchange, the minimum spacing of the partition determined by Tn is O(1/n).

### Rank two interval exchange transformations

Abstract We consider interval exchange transformations T for which the lengths of the exchanged intervals have linear rank 2 over the field of rationals. We prove that, for such T, minimality implies

### Mild mixing of certain interval-exchange transformations

• D. Robertson
• Mathematics
Ergodic Theory and Dynamical Systems
• 2017
We prove that irreducible, linearly recurrent, type W interval-exchange transformations are always mild mixing. For every irreducible permutation, the set of linearly recurrent interval-exchange

### A condition for unique ergodicity of minimal symbolic flows

Abstract A sufficient condition for unique ergodicity of symbolic flows is provided. In an important but special case of interval exchange transformations, the condition has already been validated by

### A criterion for a process to be prime

A criterion for a measure preserving transformation to be “prime” is given. The criterion allows the transformation to have uncountable centralizer.