{"id":"https://openalex.org/W4385416812","doi":"https://doi.org/10.3390/e25081149","title":"Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics","display_name":"Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics","publication_year":2023,"publication_date":"2023-07-31","ids":{"openalex":"https://openalex.org/W4385416812","doi":"https://doi.org/10.3390/e25081149","pmid":"https://pubmed.ncbi.nlm.nih.gov/37628179"},"language":"en","primary_location":{"id":"doi:10.3390/e25081149","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e25081149","pdf_url":"https://www.mdpi.com/1099-4300/25/8/1149/pdf?version=1690868087","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/8/1149/pdf?version=1690868087","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073587951","display_name":"Vlad Ghizdov\u0103\u0163","orcid":"https://orcid.org/0000-0001-8233-8862"},"institutions":[{"id":"https://openalex.org/I304011483","display_name":"Grigore T. Popa University of Medicine and Pharmacy","ror":"https://ror.org/03hd30t45","country_code":"RO","type":"education","lineage":["https://openalex.org/I304011483"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Vlad Ghizdovat","raw_affiliation_strings":["Department of Biophysics and Medical Physics, \u201cGrigore T. Popa\u201d University of Medicine and Pharmacy, 700115 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biophysics and Medical Physics, \u201cGrigore T. Popa\u201d University of Medicine and Pharmacy, 700115 Iasi, Romania","institution_ids":["https://openalex.org/I304011483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003370215","display_name":"Oana Rusu","orcid":"https://orcid.org/0000-0002-5522-2861"},"institutions":[{"id":"https://openalex.org/I4210108695","display_name":"Gheorghe Asachi Technical University of Ia\u0219i","ror":"https://ror.org/014zxnz40","country_code":"RO","type":"education","lineage":["https://openalex.org/I4210108695"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Oana Rusu","raw_affiliation_strings":["Faculty of Material Science and Engineering, \u201cGheorghe Asachi\u201d University of Iasi, 700050 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Material Science and Engineering, \u201cGheorghe Asachi\u201d University of Iasi, 700050 Iasi, Romania","institution_ids":["https://openalex.org/I4210108695"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079003078","display_name":"Mihail Fr\u0103sil\u0103","orcid":null},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Mihail Frasila","raw_affiliation_strings":["Faculty of Physics, \u201cAlexandru Ioan Cuza\u201d University of Iasi, 700050 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, \u201cAlexandru Ioan Cuza\u201d University of Iasi, 700050 Iasi, Romania","institution_ids":["https://openalex.org/I138164181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026503755","display_name":"Cristina Marcela Rusu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108695","display_name":"Gheorghe Asachi Technical University of Ia\u0219i","ror":"https://ror.org/014zxnz40","country_code":"RO","type":"education","lineage":["https://openalex.org/I4210108695"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Cristina Marcela Rusu","raw_affiliation_strings":["Department of Physics, \u201cGheorghe Asachi\u201d Technical University of Iasi, 700050 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, \u201cGheorghe Asachi\u201d Technical University of Iasi, 700050 Iasi, Romania","institution_ids":["https://openalex.org/I4210108695"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001789544","display_name":"Maricel Agop","orcid":"https://orcid.org/0000-0003-2293-5803"},"institutions":[{"id":"https://openalex.org/I33800924","display_name":"Academia Oamenilor de \u0218tiin\u021b\u0103 din Rom\u00e2nia","ror":"https://ror.org/04ybnj478","country_code":"RO","type":"facility","lineage":["https://openalex.org/I33800924"]},{"id":"https://openalex.org/I4210108695","display_name":"Gheorghe Asachi Technical University of Ia\u0219i","ror":"https://ror.org/014zxnz40","country_code":"RO","type":"education","lineage":["https://openalex.org/I4210108695"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Maricel Agop","raw_affiliation_strings":["Department of Physics, \u201cGheorghe Asachi\u201d Technical University of Iasi, 700050 Iasi, Romania","Romanian Scientists Academy, 54 Splaiul Independentei, 050094 Bucharest, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, \u201cGheorghe Asachi\u201d Technical University of Iasi, 700050 Iasi, Romania","institution_ids":["https://openalex.org/I4210108695"]},{"raw_affiliation_string":"Romanian Scientists Academy, 54 Splaiul Independentei, 050094 Bucharest, Romania","institution_ids":["https://openalex.org/I33800924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037440558","display_name":"Decebal Vasincu","orcid":"https://orcid.org/0000-0002-7139-0304"},"institutions":[{"id":"https://openalex.org/I304011483","display_name":"Grigore T. Popa University of Medicine and Pharmacy","ror":"https://ror.org/03hd30t45","country_code":"RO","type":"education","lineage":["https://openalex.org/I304011483"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Decebal Vasincu","raw_affiliation_strings":["Faculty of Dental Medicine, University of Medicine and Farmacy Grigore T. Popa Ia\u0219i, 700050 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Dental Medicine, University of Medicine and Farmacy Grigore T. Popa Ia\u0219i, 700050 Iasi, Romania","institution_ids":["https://openalex.org/I304011483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5001789544"],"corresponding_institution_ids":["https://openalex.org/I33800924","https://openalex.org/I4210108695"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09137923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"8","first_page":"1149","last_page":"1149"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9968000054359436,"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":0.9968000054359436,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9850999712944031,"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/T13650","display_name":"Computational Physics and Python Applications","score":0.9850000143051147,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/theory-of-relativity","display_name":"Theory of relativity","score":0.6696636080741882},{"id":"https://openalex.org/keywords/general-relativity","display_name":"General relativity","score":0.618226170539856},{"id":"https://openalex.org/keywords/introduction-to-the-mathematics-of-general-relativity","display_name":"Introduction to the mathematics of general relativity","score":0.581850528717041},{"id":"https://openalex.org/keywords/four-force","display_name":"Four-force","score":0.5126861333847046},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.49469372630119324},{"id":"https://openalex.org/keywords/mathematics-of-general-relativity","display_name":"Mathematics of general relativity","score":0.46695953607559204},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.45422959327697754},{"id":"https://openalex.org/keywords/multifractal-system","display_name":"Multifractal system","score":0.4312765598297119},{"id":"https://openalex.org/keywords/doubly-special-relativity","display_name":"Doubly special relativity","score":0.4312679171562195},{"id":"https://openalex.org/keywords/problem-of-time","display_name":"Problem of time","score":0.43047279119491577},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40211808681488037},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.38750267028808594},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3407246768474579},{"id":"https://openalex.org/keywords/quantum-gravity","display_name":"Quantum gravity","score":0.3353172540664673},{"id":"https://openalex.org/keywords/numerical-relativity","display_name":"Numerical relativity","score":0.21245548129081726},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.19356459379196167},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18102699518203735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1662541925907135}],"concepts":[{"id":"https://openalex.org/C149324446","wikidata":"https://www.wikidata.org/wiki/Q43514","display_name":"Theory of relativity","level":2,"score":0.6696636080741882},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.618226170539856},{"id":"https://openalex.org/C165748483","wikidata":"https://www.wikidata.org/wiki/Q6058963","display_name":"Introduction to the mathematics of general relativity","level":4,"score":0.581850528717041},{"id":"https://openalex.org/C200028538","wikidata":"https://www.wikidata.org/wiki/Q5474919","display_name":"Four-force","level":3,"score":0.5126861333847046},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.49469372630119324},{"id":"https://openalex.org/C70669116","wikidata":"https://www.wikidata.org/wiki/Q2537157","display_name":"Mathematics of general relativity","level":4,"score":0.46695953607559204},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.45422959327697754},{"id":"https://openalex.org/C133905733","wikidata":"https://www.wikidata.org/wiki/Q2629238","display_name":"Multifractal system","level":3,"score":0.4312765598297119},{"id":"https://openalex.org/C14510692","wikidata":"https://www.wikidata.org/wiki/Q3424284","display_name":"Doubly special relativity","level":4,"score":0.4312679171562195},{"id":"https://openalex.org/C4621756","wikidata":"https://www.wikidata.org/wiki/Q18344764","display_name":"Problem of time","level":4,"score":0.43047279119491577},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40211808681488037},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.38750267028808594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3407246768474579},{"id":"https://openalex.org/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.3353172540664673},{"id":"https://openalex.org/C44715290","wikidata":"https://www.wikidata.org/wiki/Q13012237","display_name":"Numerical relativity","level":3,"score":0.21245548129081726},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.19356459379196167},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18102699518203735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1662541925907135}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25081149","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e25081149","pdf_url":"https://www.mdpi.com/1099-4300/25/8/1149/pdf?version=1690868087","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":"pmid:37628179","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37628179","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10453005","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10453005","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10453005/pdf/entropy-25-01149.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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 (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:4733c9f9c159455e8b881bd865c147b3","is_oa":true,"landing_page_url":"https://doaj.org/article/4733c9f9c159455e8b881bd865c147b3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"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 25, Iss 8, p 1149 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/25/8/1149/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25081149","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 25; Issue 8; Pages: 1149","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e25081149","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e25081149","pdf_url":"https://www.mdpi.com/1099-4300/25/8/1149/pdf?version=1690868087","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":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385416812.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W932776612","https://openalex.org/W1481170646","https://openalex.org/W1494563177","https://openalex.org/W1504244791","https://openalex.org/W1966509080","https://openalex.org/W1969454151","https://openalex.org/W1994893457","https://openalex.org/W2032258166","https://openalex.org/W2039117838","https://openalex.org/W2040203580","https://openalex.org/W2075451449","https://openalex.org/W2103376451","https://openalex.org/W2158026206","https://openalex.org/W2175980532","https://openalex.org/W2259553937","https://openalex.org/W2277533584","https://openalex.org/W2506806578","https://openalex.org/W2801192398","https://openalex.org/W2910280834","https://openalex.org/W2972665969","https://openalex.org/W3012440061","https://openalex.org/W3038075476","https://openalex.org/W3148552254","https://openalex.org/W3215889318","https://openalex.org/W4206439116","https://openalex.org/W4214914059","https://openalex.org/W4251077687","https://openalex.org/W4252809977"],"related_works":["https://openalex.org/W2044510039","https://openalex.org/W2376099658","https://openalex.org/W824693400","https://openalex.org/W2964057352","https://openalex.org/W2953192518","https://openalex.org/W3024571942","https://openalex.org/W3106457011","https://openalex.org/W2073688763","https://openalex.org/W2033343758","https://openalex.org/W4385416812"],"abstract_inverted_index":{"Some":[0],"possible":[1],"correspondences":[2],"between":[3],"the":[4,9,17,22,27,39,60,81],"Scale":[5,23,55],"Relativity":[6,24,29,87],"Theory":[7,11,25],"and":[8,26,49,88],"Space-Time":[10],"can":[12,76],"be":[13],"established.":[14],"Since":[15],"both":[16],"multifractal":[18],"Schr\u00f6dinger":[19],"equation":[20],"from":[21],"General":[28,47],"equations":[30],"for":[31],"a":[32,51,69],"gravitational":[33],"field":[34],"with":[35],"axial":[36],"symmetry":[37],"accept":[38],"same":[40],"SL(2R)-type":[41],"invariance,":[42],"an":[43],"Ernst-type":[44],"potential":[45],"(from":[46,54],"Relativity)":[48,56],"also":[50],"multi-fractal":[52],"tensor":[53],"are":[57],"highlighted":[58],"in":[59,80],"description":[61,71],"of":[62,72,83],"complex":[63,73],"systems":[64,74],"dynamics.":[65],"In":[66],"this":[67],"way,":[68],"non-differentiable":[70],"dynamics":[75],"become":[77],"functional,":[78],"even":[79],"case":[82],"standard":[84],"theories":[85],"(General":[86],"Quantum":[89],"Mechanics).":[90]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}