@article{15064,
  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.},
  author       = {Bauer, U. and Edelsbrunner, Herbert and Jablonski, Grzegorz and Mrozek, M.},
  issn         = {2367-1734},
  journal      = {Journal of Applied and Computational Topology},
  number       = {4},
  pages        = {455--480},
  publisher    = {Springer Nature},
  title        = {{Čech-Delaunay gradient flow and homology inference for self-maps}},
  doi          = {10.1007/s41468-020-00058-8},
  volume       = {4},
  year         = {2020},
}