Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: University of Bologna
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: European Commission, NextGenerationEU
Award: G972786147
OpenAlex ID: W4417287267
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