# An upper bound on the dimension of the Rauzy gasket

@inproceedings{Pollicott2021AnUB, title={An upper bound on the dimension of the Rauzy gasket}, author={Mark Pollicott and Benedict Sewell}, year={2021} }

In this note, we give an elementary proof that the Hausdorff dimension of the Rauzy gasket is at most 1.7407, improving upon results of Avila et al. and Fougeron.

## One Citation

### Dynamical Systems Around the Rauzy Gasket and Their Ergodic Properties

- MathematicsInternational Mathematics Research Notices
- 2022

At the beginning of the 80s, H. Masur and W. Veech started the study of generic properties of interval exchange transformations (IETs) proving that almost every such transformation is uniquely…

## References

SHOWING 1-10 OF 14 REFERENCES

### On the Hausdorff dimension of the Rauzy gasket

- Mathematics
- 2013

In this paper, we prove that the Hausdorff dimension of the Rauzy gasket is less than 2. By this result, we answer a question addressed by Pierre Arnoux. Also, this question is a very particular case…

### Lower bounds on the dimension of the Rauzy gasket

- MathematicsBulletin de la Société mathématique de France
- 2020

The Rauzy gasket $R$ is the maximal invariant set of a certain renormalization procedure for special systems of isometries naturally appearing in the context of Novikov's problem in conductivity…

### An asymptotic formula for integer points on Markoff-Hurwitz varieties

- MathematicsAnnals of Mathematics
- 2019

We establish an asymptotic formula for the number of integer solutions to the Markoff-Hurwitz equation
x21+x22+⋯+x2n=ax1x2⋯xn+k.
When n≥4, the previous best result is by Baragar (1998) that gives…

### Geometry of plane sections of the infinite regular skew polyhedron {4, 6 | 4}

- Mathematics
- 2008

The asymptotic behavior of open plane sections of triply periodic surfaces is dictated, for an open dense set of plane directions, by an integer second homology class of the three-torus. The…

### Dynamical properties of simplicial systems and continued fraction algorithms

- Mathematics, Computer Science
- 2020

A new point of view on multidimensional continued fraction algorithms inspired by Rauzy induction is proposed and a unified proof of ergodicity for these classical examples as well as new results such as uniqueness of the measure of maximal entropy on a canonical suspension.

### Triangle Tiling Billiards and the Exceptional Family of their Escaping Trajectories: Circumcenters and Rauzy Gasket

- MathematicsExp. Math.
- 2022

Abstract Consider a periodic tiling of a plane by equal triangles obtained from the equilateral tiling by a linear transformation. We study a following tiling billiard: a ball follows straight…

### Représentation géométrique de suites de complexité $2n+1$

- Mathematics
- 1991

— We prove that ail minimal séquences of complexity 2n+ 1, satisfying to a combinatorial condition, can be represented by an interval exchange on six intervais; this generalizes a classical resuit on…

### Dynamical Systems, Topology, and Conductivity in Normal Metals

- Physics
- 2003

We present here a complete description of all asymptotic regimes of conductivity in the so-called “Geometric Strong Magnetic Field limit” in the 3D single crystal normal metals with topologically…

### Fractal geometry

- Psychology
- 1989

Editor's note: The following articles by Steven G. Krantz and Benoit B. Mandelbrot have an unusual history. In the fall of 1988, Krantz asked the Bulletin of the American Mathematical Society Book…

### Introduction to Probability

- Mathematics, Philosophy
- 1997

The articles [8], [9], [4], [7], [6], [2], [5], [1], and [3] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: E denotes a non empty set, a…