2022
DOI: 10.48550/arxiv.2206.10198
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Topological Inference of the Conley Index

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 pair… Show more

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“…One of the principal drawbacks discussed in [76] is the computational cost of computing persistent homology in degrees higher than 1 for the Vietoris-Rips complexes of large pointclouds. One idea is to more directly focus on finding critical points and Morse indices in a local neighbourhood, as in [155],…”
Section: Future Workmentioning
confidence: 99%
“…One of the principal drawbacks discussed in [76] is the computational cost of computing persistent homology in degrees higher than 1 for the Vietoris-Rips complexes of large pointclouds. One idea is to more directly focus on finding critical points and Morse indices in a local neighbourhood, as in [155],…”
Section: Future Workmentioning
confidence: 99%