# Global linearization of asymptotically stable systems without hyperbolicity

arXiv: https://arxiv.org/abs/2502.07708 · HTML: https://mlsanity.com/paper/2502.07708/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2025.

## Built on by (most cited first, 1 of 1)

- [Autoencoding Dynamics: Topological Limitations and Capabilities](https://mlsanity.com/paper/2511.04807/) (2025)

## Abstract (arXiv)

We give a proof of an extension of the Hartman-Grobman theorem to nonhyperbolic but asymptotically stable equilibria of vector fields. Moreover, the linearizing topological conjugacy is (i) defined on the entire basin of attraction if the vector field is complete, and (ii) a Ck≥ 1-diffeomorphism on the complement of the equilibrium if the vector field is Ck and the underlying space is not 5-dimensional. We also show that the Ck statement in the 5-dimensional case is equivalent to the 4-dimensional smooth Poincar'e conjecture.