{"id":"https://openalex.org/W7225586376","doi":"https://doi.org/10.67268/1812-5093-2026-34-1s-148-154","title":"Isochrones of systems with a small parameter that are independent of it","display_name":"Isochrones of systems with a small parameter that are independent of it","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225586376","doi":"https://doi.org/10.67268/1812-5093-2026-34-1s-148-154"},"language":"en","primary_location":{"id":"doi:10.67268/1812-5093-2026-34-1s-148-154","doi":"https://doi.org/10.67268/1812-5093-2026-34-1s-148-154","is_oa":true,"landing_page_url":"https://doi.org/10.67268/1812-5093-2026-34-1s-148-154","pdf_url":"https://mathnas.ejournal.by/jour/article/download/192/94","source":{"id":"https://openalex.org/S7407059500","display_name":"Proceedings of the Institute of Mathematics of the NAS of Belarus","issn_l":"1812-5093","issn":["1812-5093"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Institute of Mathematics of the NAS of Belarus","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://mathnas.ejournal.by/jour/article/download/192/94","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161269458","display_name":"A. E. Roudenok","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I291386647","display_name":"Belarusian State University","ror":"https://ror.org/021036w13","country_code":"BY","type":"education","lineage":["https://openalex.org/I291386647"]}],"countries":["BY"],"is_corresponding":false,"raw_author_name":"A. E. Roudenok","raw_affiliation_strings":["Belarusian State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Belarusian State University","institution_ids":["https://openalex.org/I291386647"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040226174","display_name":"\u041c. \u041d. \u0412\u0430\u0441\u0438\u043b\u0435\u0432\u0438\u0447","orcid":"https://orcid.org/0000-0001-6618-8649","observed_orcids":["https://orcid.org/0000-0001-6618-8649"]},"institutions":[{"id":"https://openalex.org/I291386647","display_name":"Belarusian State University","ror":"https://ror.org/021036w13","country_code":"BY","type":"education","lineage":["https://openalex.org/I291386647"]}],"countries":["BY"],"is_corresponding":false,"raw_author_name":"M. N. Vasilevich","raw_affiliation_strings":["Belarusian State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Belarusian State University","institution_ids":["https://openalex.org/I291386647"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I291386647"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"1s","first_page":"148","last_page":"154"},"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":0.9976000189781189,"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":0.9976000189781189,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0007999999797903001,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/isochronous-centers","display_name":"isochronous centers","score":0.8399999737739563},{"id":"https://openalex.org/keywords/small-parameter","display_name":"small parameter","score":0.5040000081062317},{"id":"https://openalex.org/keywords/singular-points","display_name":"singular points","score":0.6970000267028809},{"id":"https://openalex.org/keywords/second-order-nonlinearity","display_name":"quadratic nonlinearity","score":0.8429999947547913},{"id":"https://openalex.org/keywords/phase-portraits","display_name":"phase portraits","score":0.8040000200271606}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.6129999756813049},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5659999847412109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5509999990463257},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.5408999919891357},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.5365999937057495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4787999987602234},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.47679999470710754},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.47200000286102295},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4715000092983246},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.44440001249313354},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.38909998536109924},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.37209999561309814},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33500000834465027},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3149999976158142},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C2983524802","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic model","level":3,"score":0.2994999885559082},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.2937000095844269},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29190000891685486},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C9628104","wikidata":"https://www.wikidata.org/wiki/Q788009","display_name":"Autonomous system (mathematics)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.67268/1812-5093-2026-34-1s-148-154","doi":"https://doi.org/10.67268/1812-5093-2026-34-1s-148-154","is_oa":true,"landing_page_url":"https://doi.org/10.67268/1812-5093-2026-34-1s-148-154","pdf_url":"https://mathnas.ejournal.by/jour/article/download/192/94","source":{"id":"https://openalex.org/S7407059500","display_name":"Proceedings of the Institute of Mathematics of the NAS of Belarus","issn_l":"1812-5093","issn":["1812-5093"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Institute of Mathematics of the NAS of Belarus","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.67268/1812-5093-2026-34-1s-148-154","doi":"https://doi.org/10.67268/1812-5093-2026-34-1s-148-154","is_oa":true,"landing_page_url":"https://doi.org/10.67268/1812-5093-2026-34-1s-148-154","pdf_url":"https://mathnas.ejournal.by/jour/article/download/192/94","source":{"id":"https://openalex.org/S7407059500","display_name":"Proceedings of the Institute of Mathematics of the NAS of Belarus","issn_l":"1812-5093","issn":["1812-5093"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Institute of Mathematics of the NAS of Belarus","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225586376.pdf","grobid_xml":"https://content.openalex.org/works/W7225586376.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1982717554"],"related_works":["https://openalex.org/W1973368865","https://openalex.org/W2033065301","https://openalex.org/W1968570544","https://openalex.org/W1681191376","https://openalex.org/W7115028413","https://openalex.org/W4302803940","https://openalex.org/W2019913171","https://openalex.org/W3003736603","https://openalex.org/W2062784072","https://openalex.org/W2137010493"],"abstract_inverted_index":{"We":[0,46,104],"consider":[1],"an":[2],"autonomous":[3],"system":[4,39,65,70],"on":[5,92],"the":[6,32,38,55,61,64,78,86,111,125],"plane":[7],"involving":[8],"a":[9,17,22,26,29,69],"parameter":[10,79,87],"$\\lambda":[11,80,88],"$,":[12],"commonly":[13],"referred":[14],"to":[15,68],"as":[16,54],"small":[18],"parameter,":[19],"and":[20,118,129],"with":[21,71,107],"singular":[23,44],"point":[24],"(either":[25],"center":[27],"or":[28],"focus)":[30],"at":[31,42],"origin.":[33],"It":[34],"is":[35,40,100],"assumed":[36],"that":[37,49,98,114],"isochronous":[41,127],"this":[43,84],"point.":[45],"also":[47,133],"assume":[48],"its":[50],"isochrones":[51,131],"\u2013":[52,74],"defined":[53],"pre-images":[56],"of":[57,77,124],"radial":[58],"lines":[59],"under":[60,66],"transformation":[62],"from":[63],"consideration":[67],"uniform":[72],"isochronicity":[73],"are":[75,132],"independent":[76],"$.":[81],"Thus,":[82],"in":[83,97,110],"paper,":[85],"$":[89],"may":[90],"take":[91],"any":[93],"real":[94],"value":[95],"and,":[96],"sense,":[99],"not":[101],"actually":[102],"small.":[103],"construct":[105],"systems":[106],"quadratic":[108],"nonlinearities":[109],"right-hand":[112],"side":[113],"satisfy":[115],"these":[116],"requirements":[117],"determine":[119],"their":[120,130],"isochrones.":[121],"Phase":[122],"portraits":[123],"resulting":[126],"foci":[128],"constructed.":[134]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}