7 citations · 37 across the 15 of their papers we have counts for
15 papers
The small growth invariants of Goursat distributions
Susan Jane Colley, Gary Kennedy, Corey Shanbrom
This is the second of a pair of papers devoted to the local invariants of Goursat distributions. The study of these distributions naturally leads to a tower of spaces over an arbit…
The structural invariants of Goursat distributions
Susan Jane Colley, Gary Kennedy, Corey Shanbrom
This is the first of a pair of papers devoted to the local invariants of Goursat distributions. The study of these distributions naturally leads to a tower of spaces over an arbitr…
A look at endemic equilibria of compartmental epidemiological models and model control via vaccination and mitigation
Monique Chyba, Taylor Klotz, Yuriy Mileyko +1
Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the class…
Geometric methods for efficient planar swimming of copepod nauplii
Jonas Balisacan, Monique Chyba, Corey Shanbrom +1
Copepod nauplii are larval crustaceans with important ecological functions. Due to their small size, they experience an environment of low Reynolds number within their aquatic habi…
An introduction to the Kepler-Heisenberg problem
Corey Shanbrom
Here we provide an overview of what is known, and what is not known, about an interesting dynamical system known as the Kepler-Heisenberg problem. The main idea is to pose a versio…
Multi-agent systems for quadcopters
Richard Carney, Monique Chyba, Chris Gray +2
Unmanned Aerial Vehicles (UAVs) have been increasingly used in the context of remote sensing missions such as target search and tracking, mapping, or surveillance monitoring. In th…
Self-similarity in the Kepler-Heisenberg problem
Victor Dods, Corey Shanbrom
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the Heisenberg group, thought of as a three-dimensional sub-Riemannian manifold. The sub…
Numerical Methods and Closed Orbits in the Kepler-Heisenberg Problem
Victor Dods, Corey Shanbrom
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic…
Length spectra of sub-Riemannian metrics on compact Lie groups
András Domokos, Matthew Krauel, Vincent Pigno +2
Length spectra for Riemannian metrics are well studied, while sub-Riemannian length spectra have been largely unexplored. Here we give the length spectrum for a canonical sub-Riema…
A coarse stratification of the monster tower
Alex Castro, Susan Jane Colley, Gary Kennedy +1
The monster tower is a tower of spaces over a specified base; each space in the tower is a parameter space for curvilinear data up to a specified order. We describe and analyze a n…
Complete spelling rules for the Monster tower over three-space
Alex L Castro, Wyatt Howard, Corey Shanbrom
The Monster tower, also known as the Semple tower, is a sequence of manifolds with distributions of interest to both differential and algebraic geometers. Each manifold is a projec…
Bridges Between Subriemannian Geometry and Algebraic Geometry
Alex L Castro, Wyatt Howard, Corey Shanbrom
We consider how the problem of determining normal forms for a specific class of nonholonomic systems leads to various interesting and concrete bridges between two apparently unrela…
Periodic Orbits in the Kepler-Heisenberg Problem
Corey Shanbrom
One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our…
Keplerian Dynamics on the Heisenberg Group and Elsewhere
Richard Montgomery, Corey Shanbrom
Posing Kepler's problem of motion around a fixed "sun" requires the geometric mechanician to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamenta…
The Puiseux Characteristic of a Goursat Germ
Corey Shanbrom
Germs of Goursat distributions can be classified according to a geometric coding called an RVT code. Jean (1996) and Mormul (2004) have shown that this coding carries precisely the…