{"id":"https://openalex.org/W3047130513","doi":"https://doi.org/10.3390/sym12081300","title":"On Some Symmetries of Quadratic Systems","display_name":"On Some Symmetries of Quadratic Systems","publication_year":2020,"publication_date":"2020-08-04","ids":{"openalex":"https://openalex.org/W3047130513","doi":"https://doi.org/10.3390/sym12081300","mag":"3047130513"},"language":"en","primary_location":{"id":"doi:10.3390/sym12081300","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081300","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1300/pdf?version=1596539211","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/8/1300/pdf?version=1596539211","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030649439","display_name":"Maoan Han","orcid":"https://orcid.org/0000-0001-8792-1256"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Maoan Han","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089738777","display_name":"Tatjana Petek","orcid":"https://orcid.org/0000-0003-1715-6581"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Tatjana Petek","raw_affiliation_strings":["Center for Applied Mathematics and Theoretical Physics, SI-2000 Maribor, Slovenia","Faculty of Electrical Engineering and Computer Science, University of Maribor, SI-2000 Maribor, Slovenia","Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics and Theoretical Physics, SI-2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Faculty of Electrical Engineering and Computer Science, University of Maribor, SI-2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068448198","display_name":"Valery G. Romanovski","orcid":"https://orcid.org/0000-0002-2775-2953"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Valery G. Romanovski","raw_affiliation_strings":["Center for Applied Mathematics and Theoretical Physics, SI-2000 Maribor, Slovenia","Faculty of Electrical Engineering and Computer Science, University of Maribor, SI-2000 Maribor, Slovenia","Faculty of Natural Science and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia"],"raw_orcid":"https://orcid.org/0000-0002-2775-2953","affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics and Theoretical Physics, SI-2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Faculty of Electrical Engineering and Computer Science, University of Maribor, SI-2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Faculty of Natural Science and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089738777"],"corresponding_institution_ids":["https://openalex.org/I37696226","https://openalex.org/I4210106342"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.19024021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"8","first_page":"1300","last_page":"1300"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9991000294685364,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9980999827384949,"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/equivariant-map","display_name":"Equivariant map","score":0.8836115002632141},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.7002610564231873},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6164459586143494},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6104736328125},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.5803390145301819},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.5443021059036255},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5369462966918945},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5067422986030579},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5042961835861206},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.486825168132782},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48196694254875183},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.45732370018959045},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4381183385848999},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4345908761024475},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.41062843799591064},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2693396806716919},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12834405899047852},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.088340163230896},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07218173146247864}],"concepts":[{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.8836115002632141},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.7002610564231873},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6164459586143494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6104736328125},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.5803390145301819},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.5443021059036255},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5369462966918945},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5067422986030579},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5042961835861206},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.486825168132782},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48196694254875183},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.45732370018959045},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4381183385848999},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4345908761024475},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.41062843799591064},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2693396806716919},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12834405899047852},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.088340163230896},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07218173146247864},{"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12081300","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081300","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1300/pdf?version=1596539211","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e84c38da2c8e4636bcd1e11a867b9334","is_oa":true,"landing_page_url":"https://doaj.org/article/e84c38da2c8e4636bcd1e11a867b9334","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":"Symmetry, Vol 12, Iss 8, p 1300 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/8/1300/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12081300","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12081300","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081300","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1300/pdf?version=1596539211","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W83500411","https://openalex.org/W1488435683","https://openalex.org/W1980131874","https://openalex.org/W2014412336","https://openalex.org/W2031399497","https://openalex.org/W2041926611","https://openalex.org/W2131443850","https://openalex.org/W2377807473","https://openalex.org/W2810428220","https://openalex.org/W6653989641"],"related_works":["https://openalex.org/W2069360731","https://openalex.org/W1605162252","https://openalex.org/W2138135391","https://openalex.org/W2157206025","https://openalex.org/W2138496493","https://openalex.org/W2686471609","https://openalex.org/W2015689303","https://openalex.org/W2230441834","https://openalex.org/W3026223998","https://openalex.org/W109420984"],"abstract_inverted_index":{"We":[0,31],"provide":[1],"a":[2,20],"general":[3,68],"method":[4],"for":[5,93],"identifying":[6],"real":[7],"quadratic":[8],"polynomial":[9,22,80],"dynamical":[10],"systems":[11,75],"that":[12],"can":[13],"be":[14],"transformed":[15],"to":[16,71],"symmetric":[17],"ones":[18],"by":[19,38],"bijective":[21],"map":[23],"of":[24,56,62,64,74],"degree":[25],"one,":[26],"the":[27,60,65,94],"so-called":[28],"affine":[29,57],"map.":[30],"mainly":[32],"focus":[33],"on":[34,84],"symmetry":[35],"groups":[36],"generated":[37],"rotations,":[39],"in":[40,54,59,79],"other":[41],"words,":[42],"we":[43],"treat":[44],"equivariant":[45,48],"and":[46,89],"reversible":[47],"systems.":[49],"The":[50],"description":[51],"is":[52,87],"given":[53],"terms":[55],"varieties":[58],"space":[61],"parameters":[63,86],"system.":[66],"A":[67],"algebraic":[69],"approach":[70],"find":[72],"subfamilies":[73],"having":[76],"certain":[77],"symmetries":[78],"differential":[81],"families":[82],"depending":[83],"many":[85],"proposed":[88],"computer":[90],"algebra":[91],"computations":[92],"planar":[95],"case":[96],"are":[97],"presented.":[98]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}