Yim, Ka Man  ORCID: https://orcid.org/0000-0003-4736-3151 and Nanda, Vidit
2025.
Topological inference of the Conley index.
Journal of Dynamics and Differential Equations
37
, pp. 1565-1597.
10.1007/s10884-023-10310-1
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Abstract
The Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of any compact, connected isolated critical set of such a function with high confidence from a sufficiently large finite point sample. The main construction of this paper is a specific index pair which is local to the critical set in question. We establish that these index pairs have positive reach and hence admit a sampling theory for robust homology inference. This allows us to estimate the Conley index, and as a direct consequence, we are also able to estimate the Morse index of any critical point of a Morse function using finitely many local evaluations.
| Item Type: | Article |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Publisher: | Springer |
| ISSN: | 1040-7294 |
| Funders: | MR/W01176X/1 |
| Date of First Compliant Deposit: | 23 September 2023 |
| Date of Acceptance: | 28 August 2023 |
| Last Modified: | 03 Jun 2025 13:34 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/162696 |
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