{"id":"https://openalex.org/W2080846230","doi":"https://doi.org/10.3390/e11020249","title":"Generalised Entropy of Curves for the Analysis and Classification of Dynamical Systems","display_name":"Generalised Entropy of Curves for the Analysis and Classification of Dynamical Systems","publication_year":2009,"publication_date":"2009-04-29","ids":{"openalex":"https://openalex.org/W2080846230","doi":"https://doi.org/10.3390/e11020249","mag":"2080846230"},"language":"en","primary_location":{"id":"doi:10.3390/e11020249","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e11020249","pdf_url":"https://www.mdpi.com/1099-4300/11/2/249/pdf?version=1424784663","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/11/2/249/pdf?version=1424784663","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108444192","display_name":"Aldo Balestrino","orcid":null},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Aldo Balestrino","raw_affiliation_strings":["Department of Electrical Systems and Automation, University of Pisa, Via Diotisalvi 2, 56100, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Systems and Automation, University of Pisa, Via Diotisalvi 2, 56100, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079569776","display_name":"Andrea Caiti","orcid":"https://orcid.org/0000-0002-5780-3299"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Caiti","raw_affiliation_strings":["Department of Electrical Systems and Automation, University of Pisa, Via Diotisalvi 2, 56100, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Systems and Automation, University of Pisa, Via Diotisalvi 2, 56100, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066462569","display_name":"Emanuele Crisostomi","orcid":"https://orcid.org/0000-0002-7973-6357"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Emanuele Crisostomi","raw_affiliation_strings":["Department of Electrical Systems and Automation, University of Pisa, Via Diotisalvi 2, 56100, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Systems and Automation, University of Pisa, Via Diotisalvi 2, 56100, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066462569"],"corresponding_institution_ids":["https://openalex.org/I108290504"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9795,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.77060865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","issue":"2","first_page":"249","last_page":"270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10044","display_name":"Protein Structure and Dynamics","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6653033494949341},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6141886115074158},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.586329460144043},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.572231650352478},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5379825830459595},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5278917551040649},{"id":"https://openalex.org/keywords/phase-plane","display_name":"Phase plane","score":0.49624186754226685},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4878718852996826},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33551090955734253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22430425882339478},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11902639269828796},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09532555937767029},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07117453217506409}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6653033494949341},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6141886115074158},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.586329460144043},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.572231650352478},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5379825830459595},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5278917551040649},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.49624186754226685},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4878718852996826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33551090955734253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22430425882339478},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11902639269828796},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09532555937767029},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07117453217506409},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e11020249","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e11020249","pdf_url":"https://www.mdpi.com/1099-4300/11/2/249/pdf?version=1424784663","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ccbf834f2b13463ab2788b8fa78ae062","is_oa":true,"landing_page_url":"https://doaj.org/article/ccbf834f2b13463ab2788b8fa78ae062","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 11, Iss 2, Pp 249-270 (2009)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/11/2/249/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e11020249","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 11; Issue 2; Pages: 249-270","raw_type":"Text"},{"id":"pmh:oai:zenodo.org:60102","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/60102","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/e11020249","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e11020249","pdf_url":"https://www.mdpi.com/1099-4300/11/2/249/pdf?version=1424784663","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2080846230.pdf","grobid_xml":"https://content.openalex.org/works/W2080846230.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W25761614","https://openalex.org/W110826557","https://openalex.org/W122965473","https://openalex.org/W146295076","https://openalex.org/W1588211740","https://openalex.org/W1667306093","https://openalex.org/W1802223359","https://openalex.org/W1876456565","https://openalex.org/W1970650503","https://openalex.org/W1981402762","https://openalex.org/W1986254657","https://openalex.org/W1995875735","https://openalex.org/W2000983461","https://openalex.org/W2004021828","https://openalex.org/W2012315426","https://openalex.org/W2032060187","https://openalex.org/W2036547913","https://openalex.org/W2057001158","https://openalex.org/W2062196963","https://openalex.org/W2062908485","https://openalex.org/W2097599631","https://openalex.org/W2098562274","https://openalex.org/W2112396687","https://openalex.org/W2133713273","https://openalex.org/W2289391898","https://openalex.org/W2336900884","https://openalex.org/W2622832480","https://openalex.org/W3140968660","https://openalex.org/W3151322693","https://openalex.org/W4240009385","https://openalex.org/W6635202180","https://openalex.org/W6703332164"],"related_works":["https://openalex.org/W2004708907","https://openalex.org/W2377429601","https://openalex.org/W2386043911","https://openalex.org/W2027776969","https://openalex.org/W2374427492","https://openalex.org/W2081531990","https://openalex.org/W4245378846","https://openalex.org/W2069167073","https://openalex.org/W4385606208","https://openalex.org/W2403442222"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"a":[3,45,49,78],"new":[4],"approach":[5,120],"for":[6],"the":[7,11,22,25,33,36,64,68,75,81,84,92,95,100,144],"analysis":[8],"and":[9],"eventually":[10],"classification":[12],"of":[13,24,27,35,38,48,77,83,94,143],"dynamical":[14,79,105],"systems.":[15,118],"The":[16,119],"objective":[17],"is":[18,51,88],"pursued":[19],"by":[20,59],"extending":[21],"concept":[23],"entropy":[26,47,82],"plane":[28,39],"curves,":[29,40],"first":[30],"introduced":[31],"within":[32],"theory":[34],"thermodynamics":[37],"to":[41,53,74,90,99,122,128],"Rn":[42],"space.":[43,66],"Such":[44],"generalised":[46],"curve":[50,85],"used":[52,89],"evaluate":[54],"curves":[55],"that":[56],"are":[57,147],"obtained":[58],"connecting":[60,86],"several":[61,150],"points":[62,69],"in":[63,131],"phase":[65],"As":[67],"change":[70],"their":[71],"coordinates":[72],"according":[73],"equations":[76],"system,":[80],"them":[87],"infer":[91],"behaviour":[93],"underlying":[96],"dynamics.":[97],"According":[98],"proposed":[101,145],"method":[102,146],"all":[103],"linear":[104],"systems":[106],"evolve":[107],"at":[108],"constant":[109],"zero":[110],"entropy,":[111],"while":[112],"higher":[113],"asymptotic":[114],"values":[115],"characterise":[116],"nonlinear":[117],"proves":[121],"be":[123],"particularly":[124],"efficient":[125],"when":[126],"applied":[127],"chaotic":[129],"systems,":[130],"which":[132],"case":[133],"it":[134],"has":[135],"common":[136],"features":[137],"with":[138],"other":[139],"classic":[140],"approaches.":[141],"Performances":[142],"tested":[148],"over":[149],"benchmark":[151],"problems.":[152]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
