A generalized global Hartman-Grobman theorem for asymptotically stable semiflows
This work provides a theoretical extension for researchers in dynamical systems, but it is incremental as it builds directly on prior results.
The authors tackled the problem of extending the generalized global Hartman-Grobman theorem to discontinuous vector fields, specifically for asymptotically stable semiflows, by leveraging topological properties of Lyapunov functions, resulting in a theorem that works without assuming hyperbolicity.
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.