Toric promotion with reflections and refractions

A Adams, C Defant, J Striker - ar** trajectories: circumcenters and Rauzy gasket
P Hubert, O Paris-Romaskevich - Experimental Mathematics, 2022 - Taylor & Francis
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 segments …

Tiling billiards and Dynnikov's helicoid

O Paris-Romaskevich - Transactions of the Moscow Mathematical Society, 2021 - ams.org
Here are two problems. First, understanding the dynamics of a tiling billiard in a cyclic
quadrilateral periodic tiling. Second, describing the topology of connected components of …

Trees and flowers on a billiard table

O Paris-Romaskevich - arxiv preprint arxiv:1907.01178, 2019 - arxiv.org
In this work we completely describe the dynamics of triangle tiling billiards. In the first part of
this work, we propose a geometric approach of dynamics by introducing natural foliations …

Homology in Combinatorial Refraction Billiards

C Defant, D Liu - arxiv preprint arxiv:2502.06013, 2025 - arxiv.org
Given a graph $ G $ with vertex set $\{1,\ldots, n\} $, we can project the graphical
arrangement of $ G $ to an $(n-1) $-dimensional torus to obtain a toric hyperplane …

Symplectic Tiling Billiards, Planar Linkages, and Hyperbolic Geometry

RE Schwartz - arxiv preprint arxiv:2307.12259, 2023 - arxiv.org
The purpose of this paper is to unite two games, symplectic billiards and tiling billiards. The
new game is called symplectic tiling billiards. I will prove a result about periodic orbits of …

[PDF][PDF] Notes on Tilling billiards: Some thoughts and questions

O Paris-Romaskevich - 2019 - pa-ro.net
A tiling billiard is a mathematical model of mouvement of light in the heterogeneous medium.
Consider a tiling of the euclidian plane by polygones for which every tile t is marked by a …

[PDF][PDF] ARBRES ET FLEURS DANS LA LUMIÈRE REFRACTÉE

O PARIS-ROMASKEVICH - insmi.cnrs.fr
Les slides de mon exposé sont accessibles dans [6]. Certaines constructions décrites ci-
dessous y sont présentées à travers des vidéos (pliage, feuilletages parallèles, contraction …