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Linking combinatorial and classical dynamics : Conley index and Morse decompositions
combinatorial vector field
multivalued dynamical system
simplicial complex
discrete Morse theory
Conley theory
Morse decomposition
Conley–Morse graph
isolated invariant set
isolating block
We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F on the geometric realization of the simplicial complex. Moreover, F may be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions and Conley–Morse graphs of the combinatorial vector field give rise to isomorphic objects in the multivalued map case.
cris.lastimport.scopus | 2024-04-07T16:20:30Z | |
cris.lastimport.wos | 2024-04-10T00:21:21Z | |
dc.abstract.en | We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F on the geometric realization of the simplicial complex. Moreover, F may be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions and Conley–Morse graphs of the combinatorial vector field give rise to isomorphic objects in the multivalued map case. | pl |
dc.affiliation | Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej | pl |
dc.contributor.author | Batko, Bogdan - 256341 | pl |
dc.contributor.author | Kaczynski, Tomasz | pl |
dc.contributor.author | Mrozek, Marian - 130783 | pl |
dc.contributor.author | Wanner, Thomas | pl |
dc.date.accessioned | 2020-11-07T09:55:40Z | |
dc.date.available | 2020-11-07T09:55:40Z | |
dc.date.issued | 2020 | pl |
dc.date.openaccess | 0 | |
dc.description.accesstime | w momencie opublikowania | |
dc.description.physical | 967-1012 | pl |
dc.description.version | ostateczna wersja wydawcy | |
dc.description.volume | 20 | pl |
dc.identifier.doi | 10.1007/s10208-020-09444-1 | pl |
dc.identifier.eissn | 1615-3383 | pl |
dc.identifier.issn | 1615-3375 | pl |
dc.identifier.project | 2014/14/A/ST1/00453 | pl |
dc.identifier.project | ROD UJ / OP | pl |
dc.identifier.uri | https://ruj.uj.edu.pl/xmlui/handle/item/252940 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights | Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa | * |
dc.rights.licence | CC-BY | |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/legalcode.pl | * |
dc.share.type | inne | |
dc.subject.en | combinatorial vector field | pl |
dc.subject.en | multivalued dynamical system | pl |
dc.subject.en | simplicial complex | pl |
dc.subject.en | discrete Morse theory | pl |
dc.subject.en | Conley theory | pl |
dc.subject.en | Morse decomposition | pl |
dc.subject.en | Conley–Morse graph | pl |
dc.subject.en | isolated invariant set | pl |
dc.subject.en | isolating block | pl |
dc.subtype | Article | pl |
dc.title | Linking combinatorial and classical dynamics : Conley index and Morse decompositions | pl |
dc.title.journal | Foundations of Computational Mathematics | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |
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Except as otherwise noted, this item is licensed under the Attribution 4.0 International licence