A generalized global Hartman-Grobman theorem for asymptotically stable semiflows

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.

Technical note related to arXiv:2411.03277. To appear at ECC26