A generalized global Hartman-Grobman theorem for asymptotically stable semiflows
Dynamical Systems
2026-04-07 v5 Systems and Control
Systems and Control
Optimization and Control
Abstract
Recently, Kvalheim and Sontag provided a generalized global Hartman-Grobman theorem for equilibria under asymptotically stable continuous vector fields. By leveraging topological properties of Lyapunov functions, their theorem works without assuming hyperbolicity. We extend their theorem to a class of possibly discontinuous vector fields, in particular, to vector fields generating asymptotically stable semiflows.
Cite
@article{arxiv.2505.21401,
title = {A generalized global Hartman-Grobman theorem for asymptotically stable semiflows},
author = {Wouter Jongeneel},
journal= {arXiv preprint arXiv:2505.21401},
year = {2026}
}
Comments
Technical note related to arXiv:2411.03277. To appear at ECC26