5 citations · 9 across the 11 of their papers we have counts for
14 papers
Point Processes and Gap Statistics for Translation Surfaces
Kai Fu, Anthony Sanchez
We study the behavior of saddle connection directions on translation surfaces from the point process viewpoint. We define a direction point process for saddle connections of length…
Translation Surfaces arising from Right Regular Prisms
Xun Gong, Zuo Lin, Anthony Sanchez
We study flat metrics arising from right regular -prisms by viewing them as -differentials and analyzing their associated unfoldings. We show that the unfolding of a right re…
Quantitative finiteness of hyperplanes in hybrid manifolds
Ko W. Ohm, Anthony Sanchez
We prove a quantitative finiteness theorem for the number of totally geodesic hyperplanes of non-arithmetic hyperbolic -manifolds that arise from a gluing construction of Gromov…
An arithmetic Kontsevich--Zorich monodromy of a symmetric origami in genus 4
Xun Gong, Anthony Sanchez
We demonstrate the existence of a certain genus four origami whose Kontsevich--Zorich monodromy is arithmetic in the sense of Sarnak. The surface is interesting because its Veech g…
Effective equidistribution of large dimensional measures on affine invariant submanifolds
Anthony Sanchez
The unstable foliation, that locally is given by changing horizontal components of period coordinates, plays an important role in study of translation surfaces, including their def…
Kontsevich-Zorich monodromy groups of translation covers of some platonic solids
Rodolfo Gutiérrez-Romo, Dami Lee, Anthony Sanchez
We compute the Zariski closure of the Kontsevich-Zorich monodromy groups arising from certain square tiled surfaces that are geometrically motivated. Specifically we consider three…
An avoidance principle and Margulis functions for expanding translates of unipotent orbits
Anthony Sanchez, Juno Seong
We prove an avoidance principle for expanding translates of unipotent orbits for some semisimple homogeneous spaces. In addition, we prove a quantitative isolation result of closed…
Slope Gap Distributions of Veech Surfaces
Luis Kumanduri, Anthony Sanchez, Jane Wang
The slope gap distribution of a translation surface is a measure of how random the directions of the saddle connections on the surface are. It is known that Veech surfaces, a highl…
Gaps of saddle connection directions for some branched covers of tori
Anthony Sanchez
We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two iden…
W-measurable sensitivity of semigroup actions
Francisc Bozgan, Anthony Sanchez, Cesar E. Silva +3
This paper studies the notion of W-measurable sensitivity in the context of semigroup actions. W-measurable sensitivity is a measurable generalization of sensitive dependence on in…
Invariant Measures for Hybrid Stochastic Systems
Xavier Garcia, Jennifer Kunze, Thomas Rudelius +4
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can st…
Limit and Morse Sets for Deterministic Hybrid Systems
Kimberly Ayers, Xavier Garcia, Jennifer Kunze +4
The term "hybrid system" refers to a continuous time dynamical system that undergoes Markovian perturbations at discrete time intervals. In this paper, we find that under the right…
Generic extensions and generic Polynomials for multiplicative groups
Jorge Morales, Anthony Sanchez
Let be a finite-dimensional algebra over a finite field and let be the multiplicative group of . In this paper, we…
Subsequence Rational Ergodicity of Rank-One Transformations
Francisc Bozgan, Anthony Sanchez, Cesar E. Silva +2
We show that all rank-one transformations are subsequence boundedly rationally ergodic and that there exist rank-one transformations that are not weakly rationally ergodic.