Topological inference of the Conley index

Yim, Ka Man ORCID: https://orcid.org/0000-0003-4736-3151 and Nanda, Vidit 2023. Topological inference of the Conley index. Journal of Dynamics and Differential Equations 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:	Published Online
Status:	In Press
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:	27 Sep 2023 03:54
URI:	https://orca.cardiff.ac.uk/id/eprint/162696

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