• Corpus ID: 239009823

Minimizing entropy for translation surfaces

@inproceedings{Colognese2021MinimizingEF,
  title={Minimizing entropy for translation surfaces},
  author={Paul Colognese and Mark Pollicott},
  year={2021}
}
In this note we consider the entropy [5] of unit area translation surfaces in the SL(2,R) orbits of square tiled surfaces that are the union of squares, where the singularities occur at the vertices and the singularities have a common cone angle. We show that the entropy over such orbits is minimized at those surfaces tiled by equilateral triangles where the singularities occur precisely at the vertices. 

Figures from this paper

References

SHOWING 1-10 OF 19 REFERENCES
Systoles in translation surfaces
For a translation surface, we define the systole to be the length of the shortest saddle connection. We give a characterization of the maxima of the systole function on a stratum, and give a family
Translation surfaces and their orbit closures: An introduction for a broad audience
TLDR
This survey is an invitation for mathematicians from different backgrounds to become familiar with the subject, and top priority is given to presenting a view of the subject that is at once accessible and connected to many areas of mathematics.
Entropy and closed geodesies
  • A. Katok
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1982
Abstract We study asymptotic growth of closed geodesies for various Riemannian metrics on a compact manifold which carries a metric of negative sectional curvature. Our approach makes use of both
Differentiability and analyticity of topological entropy for Anosov and geodesic flows
SummaryIn this paper we investigate the regularity of the topological entropyhtop forCk perturbations of Anosov flows. We show that the topological entropy varies (almost) as smoothly as the
Lattices energies and variational calculus
In this thesis, we study minimization problems for discrete energies and we search to understand why a periodic structure can be a minimizer for an interaction energy, that is called a
An extraordinary origami curve
We study the origami W defined by the quaternion group of order 8 and its Teichmüller curve C (W) in the moduli space M3. We prove that W has Veech group SL2(ℤ), determine the equation of the family
Two-Dimensional Theta Functions and Crystallization among Bravais Lattices
TLDR
It is proved that if a function is completely monotonic, then the triangular lattice minimizes its energy per particle among Bravais lattices for any given density, and the global minimality is deduced, i.e., without a density constraint, of a triangular lattICE for some Lennard-Jones-type potentials and attractive-repulsive Yukawa potentials.
Chapter 8 - On the Lyapunov Exponents of the Kontsevich–Zorich Cocycle
The Laplace Transform
THE theory of Fourier integrals arises out of the elegant pair of reciprocal formulæThe Laplace TransformBy David Vernon Widder. (Princeton Mathematical Series.) Pp. x + 406. (Princeton: Princeton
Minimal theta functions
Let be a positive definite binary quadratic form with real coefficients and discriminant b2 − 4ac = −1. Among such forms, let . The Epstein zeta function of f is denned to be Rankin [7], Cassels [1],
...
1
2
...