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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…
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…