56 citations · 370 across the 46 of their papers we have counts for
48 papers
Vector Fields and Flows on Subcartesian Spaces
Yael Karshon, Eugene Lerman
This paper is part of a series of papers on differential geometry of -ringed spaces. In this paper, we study vector fields and their flows on a class of singular spaces.…
Differential forms on -ringed spaces
Eugene Lerman
We construct a complex of differential forms on a local -ringed space. The two main classes of spaces we have in mind are differential spaces in the sense of Sikorski and…
Stability and bifurcations of symmetric tops
Eugene Lerman
We study the stability and bifurcation of relative equilibria of a particle on the Lie group whose motion is governed by an invariant metric and an $SO(…
Runge-Kutta and Networks
Lee DeVille, Eugene Lerman, James Schmidt
We categorify the RK family of numerical integration methods (explicit and implicit). Namely we prove that if a pair of ODEs are related by an affine map then the corresponding dis…
Networks of hybrid open systems
Eugene Lerman, James Schmidt
We generalize the results of "Networks of open systems" by the first author to the setting of hybrid systems. In particular we introduce the notions of hybrid open systems, their n…
Left-invariant vector fields on a Lie 2-group
Eugene Lerman
A Lie 2-group is a category internal to the category of Lie groups. Consequently it is a monoidal category and a Lie groupoid. The Lie groupoid structure on gives rise to t…