2006/08/16 by Craig Calcaterra, Calcaterra, Craig
Computer Science · Engineering · #51F99 #53C12 #93B29 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.math/0608416
openalex publication_date 2006/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using families of curves to generalize vector fields, the Lie bracket is defined on a metric space, M. For M complete, versions of the local and global Frobenius theorems hold, and flows are shown to commute if and only if their bracket is zero. An example is given showing separable Hilbert space (the set of square integrable functions on R) is controllable by two elementary flows.