# Linearizability of flows by embeddings

arXiv: https://arxiv.org/abs/2305.18288 · HTML: https://mlsanity.com/paper/2305.18288/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2023.

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

- [Why should autoencoders work?](https://mlsanity.com/paper/2310.02250/) (2023)

## Abstract (arXiv)

We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on a higher-dimensional Euclidean space. We solve this problem for dynamical systems on connected state spaces that are either compact or contain at least one nonempty compact attractor, obtaining necessary and sufficient conditions for the existence of linearizing Ck embeddings for k∈ mathbbN≥ 0cup ∞. Corollaries include (i) several checkable necessary conditions for global linearizability and (ii) extensions of the Hartman-Grobman and Floquet normal form theorems beyond the classical settings. Our results open new perspectives on linearizability by establishing relationships to symmetry, topology, and invariant manifold theory.