A generalized global Hartman-Grobman theorem for asymptotically stable semiflows

Wouter Jongeneel

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arXiv · 2505.21401

A generalized global Hartman-Grobman theorem for asymptotically stable semiflows

Wouter Jongeneel

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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.

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Wouter Jongeneel. 2025-05-27. A generalized global Hartman-Grobman theorem for asymptotically stable semiflows. https://arxiv.org/abs/2505.21401

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