{"id":"https://openalex.org/W2076664574","doi":"https://doi.org/10.1137/120901271","title":"A Homoclinic Orbit in a Planar Singular ODE---A Computer Assisted Proof","display_name":"A Homoclinic Orbit in a Planar Singular ODE---A Computer Assisted Proof","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2076664574","doi":"https://doi.org/10.1137/120901271","mag":"2076664574"},"language":"en","primary_location":{"id":"doi:10.1137/120901271","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120901271","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://ruj.uj.edu.pl/xmlui/handle/item/34","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033277723","display_name":"Robert Szczelina","orcid":"https://orcid.org/0000-0001-7831-4577"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Robert Szczelina","raw_affiliation_strings":["[Jagiellonian University]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Jagiellonian University]","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085109355","display_name":"Piotr Zgliczy\u0144ski","orcid":"https://orcid.org/0000-0002-4852-0887"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Zgliczy\u0144ski","raw_affiliation_strings":["[Jagiellonian University]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Jagiellonian University]","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":null,"apc_paid":null,"fwci":1.8534,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.85686654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"3","first_page":"1541","last_page":"1565"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9973000288009644,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9973000288009644,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.8932602405548096},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.7392167448997498},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6753333806991577},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"Computer-assisted proof","score":0.6340872049331665},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.5872504711151123},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.5841643810272217},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5715543031692505},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5405548810958862},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4234717786312103},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.37477418780326843},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3600044250488281},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3421064615249634},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20108431577682495},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1469762623310089},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.12819722294807434},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07182064652442932}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.8932602405548096},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7392167448997498},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6753333806991577},{"id":"https://openalex.org/C173613240","wikidata":"https://www.wikidata.org/wiki/Q1150675","display_name":"Computer-assisted proof","level":3,"score":0.6340872049331665},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.5872504711151123},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.5841643810272217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5715543031692505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5405548810958862},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4234717786312103},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.37477418780326843},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3600044250488281},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3421064615249634},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20108431577682495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1469762623310089},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.12819722294807434},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07182064652442932},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120901271","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120901271","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:ruj.uj.edu.pl:item/34","is_oa":true,"landing_page_url":"http://ruj.uj.edu.pl/xmlui/handle/item/34","pdf_url":null,"source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ruj.uj.edu.pl:item/34","is_oa":true,"landing_page_url":"http://ruj.uj.edu.pl/xmlui/handle/item/34","pdf_url":null,"source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W44921523","https://openalex.org/W168022324","https://openalex.org/W170447982","https://openalex.org/W1509217370","https://openalex.org/W1967778555","https://openalex.org/W1970068950","https://openalex.org/W1971808848","https://openalex.org/W1982449011","https://openalex.org/W1989018928","https://openalex.org/W1996476546","https://openalex.org/W2006785992","https://openalex.org/W2010084406","https://openalex.org/W2011353941","https://openalex.org/W2021708781","https://openalex.org/W2023078666","https://openalex.org/W2028296976","https://openalex.org/W2031022267","https://openalex.org/W2036319645","https://openalex.org/W2041811673","https://openalex.org/W2048280869","https://openalex.org/W2050992837","https://openalex.org/W2056504720","https://openalex.org/W2056755069","https://openalex.org/W2060031533","https://openalex.org/W2067962848","https://openalex.org/W2073686912","https://openalex.org/W2089876099","https://openalex.org/W2091314510","https://openalex.org/W2100844196","https://openalex.org/W2121020818","https://openalex.org/W3102714580","https://openalex.org/W3102745588","https://openalex.org/W3104736809","https://openalex.org/W3182252275","https://openalex.org/W3215828263"],"related_works":["https://openalex.org/W1497977526","https://openalex.org/W2008693397","https://openalex.org/W2151523878","https://openalex.org/W3192909774","https://openalex.org/W2009763826","https://openalex.org/W2157138821","https://openalex.org/W2350473807","https://openalex.org/W3142626835","https://openalex.org/W2041282067","https://openalex.org/W2041811673"],"abstract_inverted_index":{"We":[0,48],"consider":[1],"a":[2,15,56,77,91],"family":[3],"of":[4,7,44,46,55,72],"2-dimensional":[5],"ODEs":[6],"the":[8,42,53,70,73],"form":[9],"$\\Delta_\\xi(z)z'":[10],"=":[11,66],"f_\\xi(z)$":[12],"depending":[13],"on":[14],"real":[16],"parameter":[17,63],"$\\xi$":[18],"which":[19,39],"was":[20],"investigated":[21],"by":[22],"Vladimirov":[23],"[Rep.":[24],"Math.":[25],"Phys.,":[26],"61":[27],"(2008),":[28],"pp.":[29],"381--400].":[30],"In":[31],"this":[32,83,86],"system,":[33],"there":[34],"exist":[35],"stationary":[36],"points":[37],"$p_\\xi$":[38,60],"belong":[40],"to":[41,59,69,80,90,107],"set":[43],"zeros":[45],"$\\Delta_\\xi$.":[47],"prove,":[49],"using":[50],"rigorous":[51],"numerics,":[52],"existence":[54],"homoclinic":[57],"orbit":[58],"for":[61],"some":[62,96],"value":[64],"$\\xi":[65],"\\xi_h$.":[67],"Due":[68],"singularity":[71],"system":[74,98],"it":[75],"takes":[76],"finite":[78],"time":[79],"travel":[81],"along":[82],"orbit,":[84],"and":[85],"property":[87],"gives":[88],"rise":[89],"compacton-like":[92],"traveling":[93],"wave":[94],"in":[95,111],"hydrodynamic":[97],"describing":[99],"relaxing":[100],"media.":[101],"Our":[102],"approach":[103],"could":[104],"be":[105],"used":[106],"prove":[108],"similar":[109],"results":[110],"other":[112],"singular":[113],"systems":[114],"as":[115],"well.":[116]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}