Detecting invariant manifolds of dynamical systems using persistent homology

Stavros Anastassiou; Žiga Virk

Detecting invariant manifolds of dynamical systems using persistent homology

Dynamical Systems 2026-07-07 v1 Algebraic Topology Metric Geometry

Authors: Stavros Anastassiou , Žiga Virk

Abstract

We use methods of Persistent Homology Theory to study invariant manifolds of dynamical systems. We first establish connections between the persistence diagrams of two sets which are close to each other, with respect to the Hausdorff distance. We then apply these results to study properties of limit sets of specific dynamical systems, by using the persistence diagram of a numerically obtained sample set. Under mild assumptions, we show how to use numerical data to state analytical results concerning the geometry of the limit sets.

Keywords

persistent homology invariant manifolds dynamical systems limit sets Hausdorff distance persistence diagrams

Cite

@article{arxiv.2607.05960,
  title  = {Detecting invariant manifolds of dynamical systems using persistent homology},
  author = {Stavros Anastassiou and Žiga Virk},
  journal= {arXiv preprint arXiv:2607.05960},
  year   = {2026}
}

Comments

20 pages