6 citations · 12 across the 9 of their papers we have counts for
9 papers
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…
The Length Spectrum of the Sub-Riemannian Three-Sphere
David Klapheck, Michael VanValkenburgh
We determine the lengths of all closed sub-Riemannian geodesics on the three-sphere. Our methods are elementary and allow us to avoid using explicit formulas for the sub-Riemannian…
The Pseudospectrum of the Zakharov-Shabat System
Michael VanValkenburgh
We study the pseudospectrum of the non-selfadjoint Zakharov-Shabat system in the semiclassical regime. The pseudospectrum may be defined as the union of the spectra of perturbation…
Linear Symplectomorphisms as R-Lagrangian Subspaces
J. Chris Hellmann, Brennan Langenbach, Michael VanValkenburgh
The graph of a real symplectic linear transformation is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely…
A Simple Proof of Unique Continuation for J-holomorphic Curves
Michael VanValkenburgh
In this expository paper, we prove strong unique continuation for J-holomorphic curves by first giving a simple proof of Aronszajn's theorem in the special case of the two-dimensio…
Manipulation of Semiclassical Laguerre-Gaussian Modes: a Model Case
Michael VanValkenburgh
We continue the study, from a semiclassical viewpoint, of Calvo and Picon's operators, as manipulating photon states in quantum communication. In a previous paper, we defined a one…