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, and to recover the eigenspaces of the endomorphism on homology induced by the self-map. The chain maps are constructed using discrete Morse theory for Cech and Delaunay complexes, representing the requisite discrete gradient field implicitly in order to get fast algorithms. |
Year | Venue | Field |
|---|---|---|
2017 | arXiv: Algebraic Topology | Topology,Discrete mathematics,Vector field,Persistent homology,Dynamical systems theory,Discrete Morse theory,Mathematics,Dynamical system,Endomorphism,Delaunay triangulation |
DocType | Volume | Citations |
Journal | abs/1709.04068 | 1 |
PageRank | References | Authors |
0.38 | 2 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulrich Bauer | 1 | 102 | 10.84 |
| Herbert Edelsbrunner | 2 | 6787 | 1112.29 |
| Grzegorz Jabłoński | 3 | 15 | 2.37 |
| Marian Mrozek | 4 | 176 | 24.88 |