Name
Abstract | ||
|---|---|---|
We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1007/s41468-020-00058-8 | Journal of Applied and Computational Topology |
Keywords | DocType | Volume |
Computational topology, Persistent homology, Dynamical systems, 37B99, 55N31, 65P99 | Journal | 4 |
Issue | ISSN | Citations |
4 | 2367-1726 | 1 |
PageRank | References | Authors |
0.35 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulrich Bauer | 1 | 102 | 10.84 |
| Herbert Edelsbrunner | 2 | 6787 | 1112.29 |
| G. Jabłoński | 3 | 1 | 0.35 |
| M. Mrozek | 4 | 1 | 0.35 |