8 papers
Lonely Runner Relations
Matthias Beck, Samuel Everett
We study the Lonely Runner Conjecture (LRC), conceived by Jörg M. Wills in the 1960's: Given positive integers , there exists a positive real number such…
Persistence of periodic billiard orbits under domain deformation
Samuel Everett
We prove that if a polygon admits a periodic billiard orbit satisfying a certain combinatorial criterion, then there are paths of polygons in parameter space for which every polygo…
Random tensor isomorphism under orthogonal and unitary actions
Jeremy Chizewer, Samuel Everett, Deven Mithal +1
We study the problem of testing whether two tensors in are isomorphic under the natural action of orthogonal groups $\text…
Correspondences in computational and dynamical complexity II: forcing complex reductions
Samuel Everett
An algebraic telic problem is a decision problem in formalizing finite-time reachability questions for one-dimensional dynamical systems. We prove that the…
Correspondences in computational and dynamical complexity I
Samuel Everett
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic proble…
Deciding subspace reachability problems with application to Skolem's Problem
Samuel Everett
The higher-dimensional version of Kannan and Lipton's Orbit Problem asks whether it is decidable if a target subspace can be reached from a starting point under repeated applicatio…
On the use of dynamical systems in cryptography
Samuel Everett
Ever since the link between nonlinear science and cryptography became apparent, the problem of applying chaotic dynamics to the construction of cryptographic systems has gained a b…
A geometric dynamical system with relation to billiards
Samuel Everett
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in .…