{"id":"https://openalex.org/W2805288495","doi":"https://doi.org/10.1137/17m1139606","title":"An Algorithmic Approach to Lattices and Order in Dynamics","display_name":"An Algorithmic Approach to Lattices and Order in Dynamics","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2805288495","doi":"https://doi.org/10.1137/17m1139606","mag":"2805288495"},"language":"en","primary_location":{"id":"doi:10.1137/17m1139606","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1139606","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.vu.nl/en/publications/31426daa-a7c2-4546-865b-ea8334baa060","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004040775","display_name":"William D. Kalies","orcid":"https://orcid.org/0000-0002-8228-3598"},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William D. Kalies","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431","institution_ids":["https://openalex.org/I63772739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007075956","display_name":"Dinesh Kasti","orcid":null},"institutions":[{"id":"https://openalex.org/I2802038477","display_name":"Eastern Wyoming College","ror":"https://ror.org/03ye76s02","country_code":"US","type":"education","lineage":["https://openalex.org/I2802038477"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dinesh Kasti","raw_affiliation_strings":["Department of Mathematics, Eastern Wyoming College, Torrington, WY 82240"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Eastern Wyoming College, Torrington, WY 82240","institution_ids":["https://openalex.org/I2802038477"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109092368","display_name":"Robert Vandervorst","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Vandervorst","raw_affiliation_strings":["VU University, Amsterdam, the Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"VU University, Amsterdam, the Netherlands","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1001,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.85842718,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"17","issue":"2","first_page":"1617","last_page":"1649"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9623000025749207,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9606999754905701,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.7458586692810059},{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.646942138671875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5258277654647827},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5204327702522278},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4619816243648529},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4441326856613159},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3450757563114166},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.325921893119812},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2622498869895935},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08407142758369446}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.7458586692810059},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.646942138671875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5258277654647827},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5204327702522278},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4619816243648529},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4441326856613159},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3450757563114166},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.325921893119812},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2622498869895935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08407142758369446},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1139606","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1139606","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:research.vu.nl:openaire/31426daa-a7c2-4546-865b-ea8334baa060","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/31426daa-a7c2-4546-865b-ea8334baa060","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kasti, D, Van der vorst, R C A M & Kalies, W D 2018, 'An algorithmic approach to lattices and order in dynamics', SIAM Journal on Applied Dynamical Systems, vol. 17, no. 2, pp. 1617-1649. https://doi.org/10.1137/17M1139606","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:research.vu.nl:publications/31426daa-a7c2-4546-865b-ea8334baa060","is_oa":true,"landing_page_url":"https://hdl.handle.net/1871.1/31426daa-a7c2-4546-865b-ea8334baa060","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kasti, D, Van der vorst, R C A M & Kalies, W D 2018, 'An algorithmic approach to lattices and order in dynamics', SIAM Journal on Applied Dynamical Systems, vol. 17, no. 2, pp. 1617-1649. https://doi.org/10.1137/17M1139606","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:research.vu.nl:openaire/31426daa-a7c2-4546-865b-ea8334baa060","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/31426daa-a7c2-4546-865b-ea8334baa060","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kasti, D, Van der vorst, R C A M & Kalies, W D 2018, 'An algorithmic approach to lattices and order in dynamics', SIAM Journal on Applied Dynamical Systems, vol. 17, no. 2, pp. 1617-1649. https://doi.org/10.1137/17M1139606","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6299999952316284,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G6430499662","display_name":null,"funder_award_id":"0914995","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W616063655","https://openalex.org/W1809268447","https://openalex.org/W1866328638","https://openalex.org/W1968614010","https://openalex.org/W2028617788","https://openalex.org/W2029359030","https://openalex.org/W2053436201","https://openalex.org/W2055707808","https://openalex.org/W2066967910","https://openalex.org/W2082578307","https://openalex.org/W2085511837","https://openalex.org/W2093397547","https://openalex.org/W2097894461","https://openalex.org/W2111474755","https://openalex.org/W2121020818","https://openalex.org/W2130280533","https://openalex.org/W2130816896","https://openalex.org/W2140082096","https://openalex.org/W2172178670","https://openalex.org/W2314752401","https://openalex.org/W2513283730","https://openalex.org/W2525522017","https://openalex.org/W2727020437","https://openalex.org/W2963440743"],"related_works":["https://openalex.org/W3015672237","https://openalex.org/W4308159138","https://openalex.org/W4256653909","https://openalex.org/W1979798674","https://openalex.org/W3169947911","https://openalex.org/W2990092783","https://openalex.org/W2784745440","https://openalex.org/W1878187357","https://openalex.org/W47340958","https://openalex.org/W1998601876"],"abstract_inverted_index":{"Recurrent":[0],"versus":[1],"gradient-like":[2],"behavior":[3],"in":[4,37],"global":[5],"dynamics":[6],"can":[7],"be":[8],"characterized":[9],"via":[10],"a":[11,45,48,70,75],"surjective":[12,40],"lattice":[13,41],"homomorphism":[14],"between":[15,22],"certain":[16],"bounded,":[17],"distributive":[18],"lattices,":[19],"that":[20,54,68,73,86],"is,":[21],"attracting":[23],"blocks":[24],"(or":[25],"neighborhoods)":[26],"and":[27,59,93],"attractors.":[28],"Using":[29],"this":[30],"characterization,":[31],"we":[32,64],"build":[33],"finite,":[34],"combinatorial":[35,71],"models":[36],"terms":[38],"of":[39],"homomorphisms,":[42],"which":[43],"lay":[44],"foundation":[46],"for":[47,51,78,90],"computational":[49,84],"theory":[50,89],"dynamical":[52],"systems":[53],"focuses":[55],"on":[56],"Morse":[57,76],"decompositions":[58],"index":[60],"lattices.":[61],"In":[62],"particular":[63],"present":[65],"an":[66],"algorithm":[67],"builds":[69],"model":[72],"represents":[74],"decomposition":[77],"the":[79,88],"underlying":[80],"dynamics.":[81],"We":[82],"give":[83],"examples":[85],"illustrate":[87],"both":[91],"maps":[92],"flows.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}