{"license":"https://creativecommons.org/licenses/by/4.0/","abstract":[{"text":"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.\r\n","lang":"eng"}],"isi":1,"language":[{"iso":"eng"}],"date_published":"2015-10-01T00:00:00Z","page":"1213 - 1244","file":[{"date_created":"2018-12-12T10:08:10Z","access_level":"open_access","relation":"main_file","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","content_type":"application/pdf","date_updated":"2020-07-14T12:45:26Z","file_size":1317546,"checksum":"3566f3a8b0c1bc550e62914a88c584ff","file_id":"4670","creator":"system"}],"title":"The persistent homology of a self-map","external_id":{"isi":["000360862900004"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"day":"01","citation":{"chicago":"Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” <i>Foundations of Computational Mathematics</i>. Springer, 2015. <a href=\"https://doi.org/10.1007/s10208-014-9223-y\">https://doi.org/10.1007/s10208-014-9223-y</a>.","ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.","ama":"Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. <i>Foundations of Computational Mathematics</i>. 2015;15(5):1213-1244. doi:<a href=\"https://doi.org/10.1007/s10208-014-9223-y\">10.1007/s10208-014-9223-y</a>","mla":"Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” <i>Foundations of Computational Mathematics</i>, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:<a href=\"https://doi.org/10.1007/s10208-014-9223-y\">10.1007/s10208-014-9223-y</a>.","apa":"Edelsbrunner, H., Jablonski, G., &#38; Mrozek, M. (2015). The persistent homology of a self-map. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-014-9223-y\">https://doi.org/10.1007/s10208-014-9223-y</a>","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","ieee":"H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” <i>Foundations of Computational Mathematics</i>, vol. 15, no. 5. Springer, pp. 1213–1244, 2015."},"year":"2015","file_date_updated":"2020-07-14T12:45:26Z","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7"}],"publisher":"Springer","article_processing_charge":"No","intvolume":"        15","date_created":"2018-12-11T11:55:20Z","publication_status":"published","acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the Polish National Science Center under Grant No. N201 419639.","quality_controlled":"1","doi":"10.1007/s10208-014-9223-y","department":[{"_id":"HeEd"}],"scopus_import":"1","_id":"2035","ddc":["000"],"author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Jablonski","full_name":"Jablonski, Grzegorz","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Marian","full_name":"Mrozek, Marian","last_name":"Mrozek"}],"publication":"Foundations of Computational Mathematics","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publist_id":"5022","pubrep_id":"486","status":"public","oa_version":"Published Version","month":"10","oa":1,"has_accepted_license":"1","ec_funded":1,"type":"journal_article","issue":"5","date_updated":"2025-09-23T14:08:54Z","volume":15}