{"id":"https://openalex.org/W2743785931","doi":"https://doi.org/10.1142/s0218127417501310","title":"Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields","display_name":"Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields","publication_year":2017,"publication_date":"2017-07-01","ids":{"openalex":"https://openalex.org/W2743785931","doi":"https://doi.org/10.1142/s0218127417501310","mag":"2743785931"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417501310","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417501310","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100615345","display_name":"Jing Li","orcid":"https://orcid.org/0000-0002-7278-2764"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jing Li","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019460895","display_name":"Liying Kou","orcid":null},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liying Kou","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100334967","display_name":"Duo Wang","orcid":"https://orcid.org/0000-0002-5151-1009"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Duo Wang","raw_affiliation_strings":["Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, P. R. China","School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-5151-1009","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, P. R. China","institution_ids":["https://openalex.org/I3045169105"]},{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100615345"],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":null,"apc_paid":null,"fwci":1.2715,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.78677881,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"27","issue":"08","first_page":"1750131","last_page":"1750131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9922999739646912,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7919312715530396},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.7667343616485596},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.6836870312690735},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6200001239776611},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5523977279663086},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5389123558998108},{"id":"https://openalex.org/keywords/nilpotent-matrix","display_name":"Nilpotent matrix","score":0.4434834420681},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3584004342556},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35736361145973206},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.15344980359077454},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13183021545410156},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1100434958934784},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.09810632467269897},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.07080793380737305},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0701313316822052}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7919312715530396},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.7667343616485596},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.6836870312690735},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6200001239776611},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5523977279663086},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5389123558998108},{"id":"https://openalex.org/C27563320","wikidata":"https://www.wikidata.org/wiki/Q650670","display_name":"Nilpotent matrix","level":5,"score":0.4434834420681},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3584004342556},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35736361145973206},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.15344980359077454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13183021545410156},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1100434958934784},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.09810632467269897},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.07080793380737305},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0701313316822052},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127417501310","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417501310","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8601795584","display_name":null,"funder_award_id":"11372014, 11072007,11290152,11072008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1231834888","https://openalex.org/W1515043949","https://openalex.org/W1975818603","https://openalex.org/W1977030425","https://openalex.org/W1982912308","https://openalex.org/W2003125137","https://openalex.org/W2004439991","https://openalex.org/W2033345573","https://openalex.org/W2033477867","https://openalex.org/W2034382376","https://openalex.org/W2058567340","https://openalex.org/W2084750861","https://openalex.org/W2088424770","https://openalex.org/W2158977328","https://openalex.org/W2159521032","https://openalex.org/W3105902102"],"related_works":["https://openalex.org/W4298239761","https://openalex.org/W2952902844","https://openalex.org/W2065501945","https://openalex.org/W1965214493","https://openalex.org/W2376823090","https://openalex.org/W2738937880","https://openalex.org/W2963725839","https://openalex.org/W4298352699","https://openalex.org/W2950966903","https://openalex.org/W2394272260"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,42,46,57,66,69],"unique":[4],"normal":[5,60,72],"form":[6,73],"for":[7],"a":[8,24],"class":[9],"of":[10,26,35,41,45,68],"three-dimensional":[11],"nilpotent":[12],"vector":[13,48],"fields":[14],"with":[15],"symmetry":[16],"is":[17,23,74],"investigated.":[18],"The":[19,54],"key":[20],"technique":[21],"used":[22],"combination":[25],"multiple":[27],"Lie":[28],"brackets,":[29],"linear":[30,43],"grading":[31],"function,":[32],"new":[33],"notations":[34],"block":[36],"matrices":[37],"and":[38,56,65],"first":[39,55],"integral":[40],"part":[44],"given":[47],"field":[49],"which":[50],"avoids":[51],"complicated":[52],"calculations.":[53],"second":[58,70],"order":[59,71],"forms":[61],"are":[62],"computed":[63],"successively,":[64],"uniqueness":[67],"proved":[75],"under":[76],"certain":[77],"conditions.":[78]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
