Čech-Delaunay gradient flow and homology inference for self-maps Bauer, U. Edelsbrunner, Herbert ; https://orcid.org/0000-0002-9823-6833 Jablonski, Grzegorz ; https://orcid.org/0000-0002-3536-9866 Mrozek, M. ddc:500 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. Springer Nature 2020 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/15064 https://research-explorer.ista.ac.at/download/15064/15065 Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. <i>Journal of Applied and Computational Topology</i>. 2020;4(4):455-480. doi:<a href="https://doi.org/10.1007/s41468-020-00058-8">10.1007/s41468-020-00058-8</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s41468-020-00058-8 info:eu-repo/semantics/altIdentifier/issn/2367-1726 info:eu-repo/semantics/altIdentifier/e-issn/2367-1734 info:eu-repo/semantics/openAccess