Matthew D. Kvalheim

activity

20162026

most citedGlobal linearization and fiber bundle structure of invariant manifolds

29 citations · 52 across the 16 of their papers we have counts for

collaborators

Showing 2025Show all

3 papers · 1 filter

cs.LG2025

Autoencoding Dynamics: Topological Limitations and Capabilities

Matthew D. Kvalheim, Eduardo D. Sontag

Given a "data manifold" $M \subset R^{n}$ and "latent space" $R^{ℓ}$ , an autoencoder is a pair of continuous maps consisting of an "encoder" $E\colon \mathbb{R}^n\t…

math.DS2025

Differential topology of the spaces of asymptotically stable vector fields and Lyapunov functions

Matthew D. Kvalheim

We study the topology of the space of all smooth asymptotically stable vector fields on $R^{n}$ , as well as the space of all proper smooth Lyapunov functions for such vector…

math.DS2025

Global linearization of asymptotically stable systems without hyperbolicity

Matthew D. Kvalheim, Eduardo D. Sontag

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 conjuga…