Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.
CITATION STYLE
Edelsbrunner, H., Jabłoński, G., & Mrozek, M. (2015). The Persistent Homology of a Self-Map. Foundations of Computational Mathematics, 15(5), 1213–1244. https://doi.org/10.1007/s10208-014-9223-y
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