Path signatures of ODE solutions
Algebraic Geometry
2025-05-20 v1 Differential Geometry
Abstract
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. By employing the geometric theory of nonlinear systems of ordinary differential equations, we find necessary and sufficient algebraic conditions on the signature tensors of a path to be a solution of a given system of ODEs. As an application, we describe in detail the systems of ODEs that describe the trajectories of a vector field, in particular a linear and Hamiltonian one.
Keywords
Cite
@article{arxiv.2505.13234,
title = {Path signatures of ODE solutions},
author = {Francesco Galuppi and Giovanni Moreno and Pierpaola Santarsiero},
journal= {arXiv preprint arXiv:2505.13234},
year = {2025}
}