{"id":"https://openalex.org/W4407694890","doi":"https://doi.org/10.1134/s0012266124601633","title":"Family of Logarithmic Spirals in Hamiltonian Systems of Dimension 8 with Control in a Disk","display_name":"Family of Logarithmic Spirals in Hamiltonian Systems of Dimension 8 with Control in a Disk","publication_year":2024,"publication_date":"2024-11-01","ids":{"openalex":"https://openalex.org/W4407694890","doi":"https://doi.org/10.1134/s0012266124601633"},"language":"en","primary_location":{"id":"doi:10.1134/s0012266124601633","doi":"https://doi.org/10.1134/s0012266124601633","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0012266124601633","pdf_url":null,"source":{"id":"https://openalex.org/S71958379","display_name":"Differential Equations","issn_l":"0012-2661","issn":["0012-2661","1608-3083"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Differential Equations","raw_type":"journal-article"},"volume":null,"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/A5014861478","display_name":"Mariya Igorevna Ronzhina","orcid":"https://orcid.org/0000-0002-8127-9319","observed_orcids":["https://orcid.org/0000-0002-8127-9319"]},"institutions":[{"id":"https://openalex.org/I119694697","display_name":"Gubkin Russian State University of Oil and Gas","ror":"https://ror.org/0082yr561","country_code":"RU","type":"education","lineage":["https://openalex.org/I119694697"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"M. I. Ronzhina","raw_affiliation_strings":["National University of Oil and Gas \u201cGubkin University\u201d, Moscow, 119991, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Oil and Gas \u201cGubkin University\u201d, Moscow, 119991, Russia","institution_ids":["https://openalex.org/I119694697"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112260400","display_name":"Larisa Anatol'evna Manita","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"L. A. Manita","raw_affiliation_strings":["HSE University, Moscow, 109028, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"HSE University, Moscow, 109028, Russia","institution_ids":["https://openalex.org/I118501908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014861478","https://openalex.org/A5112260400"],"corresponding_institution_ids":["https://openalex.org/I118501908","https://openalex.org/I119694697"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23944833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":"11","first_page":"1603","last_page":"1613"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.6211000084877014,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.6211000084877014,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.05849999934434891,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.05810000002384186,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/logarithmic-spiral","display_name":"logarithmic spiral","score":0.9750000238418579},{"id":"https://openalex.org/keywords/optimal-control","display_name":"optimal control","score":0.8479999899864197},{"id":"https://openalex.org/keywords/control-affine-systems","display_name":"control-affine systems","score":0.6740000247955322},{"id":"https://openalex.org/keywords/hamiltonian-systems","display_name":"Hamiltonian systems","score":0.9210000038146973},{"id":"https://openalex.org/keywords/finite-time-reachability","display_name":"finite-time reachability","score":0.5249999761581421}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8602526187896729},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6292316913604736},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6052614450454712},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6007907390594482},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5108897089958191},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4503525495529175},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4329315721988678},{"id":"https://openalex.org/C168185519","wikidata":"https://www.wikidata.org/wiki/Q5156577","display_name":"Complex dimension","level":2,"score":0.4319726228713989},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4000636339187622},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1581917405128479},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0659436583518982}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0012266124601633","doi":"https://doi.org/10.1134/s0012266124601633","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0012266124601633","pdf_url":null,"source":{"id":"https://openalex.org/S71958379","display_name":"Differential Equations","issn_l":"0012-2661","issn":["0012-2661","1608-3083"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Differential Equations","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W150313508","https://openalex.org/W1444347584","https://openalex.org/W2145061311","https://openalex.org/W2315473342","https://openalex.org/W3116916964","https://openalex.org/W3121890739","https://openalex.org/W3185700508","https://openalex.org/W4206230921","https://openalex.org/W4206297252","https://openalex.org/W4233863580","https://openalex.org/W4362702031"],"related_works":["https://openalex.org/W2046736294","https://openalex.org/W4401442391","https://openalex.org/W2980815195","https://openalex.org/W48199998","https://openalex.org/W1519526186","https://openalex.org/W2260200182","https://openalex.org/W4293584968","https://openalex.org/W2384758770","https://openalex.org/W2999616507","https://openalex.org/W4392238179"],"abstract_inverted_index":{"Abstract":[0],"We":[1,22],"study":[2],"a":[3,6,20,36,87],"neighbourhood":[4],"of":[5,41,44,49,53,66,72,77],"singular":[7,83],"second-order":[8,84],"extremal":[9,85],"in":[10,17,19,26,60,74,86],"optimal":[11],"control":[12,18,59,92],"problems":[13],"that":[14,80],"are":[15],"affine":[16],"disk.":[21,62],"consider":[23],"the":[24,28,39,42,45,50,54,61,70,75,82,91,98],"case":[25],"which":[27],"Hamiltonian":[29,51],"system":[30,52],"has":[31],"dimension":[32],"8":[33],"and":[34],"is":[35],"small":[37],"(in":[38],"sense":[40],"action":[43],"Fuller":[46,56],"group)":[47],"perturbation":[48],"generalized":[55],"problem":[57],"with":[58],"For":[63],"this":[64],"class":[65],"problems,":[67],"we":[68],"prove":[69],"existence":[71],"extremals":[73],"form":[76],"logarithmic":[78],"spirals":[79],"reach":[81],"finite":[88],"time,":[89],"while":[90],"performs":[93],"infinitely":[94],"many":[95],"rotations":[96],"around":[97],"circle.":[99]},"counts_by_year":[],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2025-10-10T00:00:00"}