3 papers
math.AP2024
The Massless Dirac Equation in Three Dimensions: Dispersive estimates and zero energy obstructions
William R. Green, Connor Lane, Benjamin Lyons +2
We investigate dispersive estimates for the massless three dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a $\langle t\rangl…
math.OC2024
Optimal Control of Hybrid Systems with Submersive Resets
William Clark, Maria Oprea, Aden Shaw
Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the opti…
math.DS2023
A Study of the Long-Term Behavior of Hybrid Systems with Symmetries via Reduction and the Frobenius-Perron Operator
Maria Oprea, Aden Shaw, Robi Huq +3
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. As typical in dynamical analysis, an essential goal is to study the long-term behavior…