{"id":"https://openalex.org/W7220929188","doi":"https://doi.org/10.48550/arxiv.2610.09176","title":"A family of Hurwitz polynomial vector fields in $\\mathbb{R}^3$ having non-constant periodic orbits","display_name":"A family of Hurwitz polynomial vector fields in $\\mathbb{R}^3$ having non-constant periodic orbits","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220929188","doi":"https://doi.org/10.48550/arxiv.2610.09176"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09176","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09176","pdf_url":"https://arxiv.org/pdf/2610.09176","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.09176","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074037622","display_name":"\u00c1lvaro Casta\u00f1eda","orcid":"https://orcid.org/0000-0002-8571-1578","observed_orcids":["https://orcid.org/0000-0002-8571-1578"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Casta\u00f1eda, \u00c1lvaro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025493391","display_name":"Salom\u00f3n Rebollo-Perdomo","orcid":"https://orcid.org/0000-0002-5526-9344","observed_orcids":["https://orcid.org/0000-0002-5526-9344"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rebollo-Perdomo, Salom\u00f3n","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.0019000000320374966,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/saddle-periodic-orbits","display_name":"saddle periodic orbits","score":0.656000018119812},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.7459999918937683},{"id":"https://openalex.org/keywords/smooth-vector-fields","display_name":"smooth vector fields","score":0.574999988079071}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7113999724388123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6973999738693237},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.6233999729156494},{"id":"https://openalex.org/C120501884","wikidata":"https://www.wikidata.org/wiki/Q1414214","display_name":"Hurwitz polynomial","level":3,"score":0.6047999858856201},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.565500020980835},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.546500027179718},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.47429999709129333},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3862999975681305},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37470000982284546},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.30790001153945923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3077000081539154},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2784000039100647},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C198931094","wikidata":"https://www.wikidata.org/wiki/Q2610096","display_name":"Hurwitz matrix","level":3,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09176","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09176","pdf_url":"https://arxiv.org/pdf/2610.09176","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.09176","doi":"https://doi.org/10.48550/arxiv.2610.09176","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09176","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09176","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09176","pdf_url":"https://arxiv.org/pdf/2610.09176","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220929188.pdf","grobid_xml":"https://content.openalex.org/works/W7220929188.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7156319427","https://openalex.org/W2053025555","https://openalex.org/W6986294895","https://openalex.org/W7061072494","https://openalex.org/W2110602566","https://openalex.org/W1973434253","https://openalex.org/W98329365","https://openalex.org/W7097020512","https://openalex.org/W2051739407","https://openalex.org/W1821716158"],"abstract_inverted_index":{"We":[0],"construct":[1],"a":[2,15,87],"two-parameter":[3],"family":[4,26],"of":[5,19,24,36,49,59,78,114],"polynomial":[6,84],"vector":[7,66,85],"fields":[8,67],"in":[9,46,63,99,109],"$\\mathbb{R}^3$":[10],"and":[11,29,39,103],"prove":[12],"that,":[13],"on":[14,52,68],"nonempty":[16],"open":[17,50],"set":[18],"parameter":[20],"values,":[21],"every":[22],"member":[23],"the":[25,57,75,92,96,100,115],"is":[27],"Hurwitz":[28,64,83],"possesses":[30],"two":[31],"non-constant":[32,60,79],"periodic":[33,61,80],"orbits,":[34],"one":[35,40],"saddle":[37],"type":[38],"attracting.":[41],"This":[42,70],"answers":[43],"Problem":[44],"19":[45],"Gasull's":[47],"list":[48],"problems":[51],"low-dimensional":[53],"dynamical":[54],"systems":[55],"concerning":[56],"existence":[58],"orbits":[62,81],"smooth":[65],"$\\mathbb{R}^3$.":[69],"also":[71],"provides":[72],"counterexamples":[73,94],"to":[74,95],"expected":[76],"non-existence":[77],"for":[82],"fields;":[86],"question":[88],"that":[89,104],"arose":[90],"from":[91],"first":[93],"Markus-Yamabe":[97],"conjecture":[98],"late":[101],"1990s":[102],"was":[105],"stated":[106],"by":[107],"Meisters":[108],"his":[110],"featured":[111],"MathSciNet":[112],"review":[113],"Bernat-Llibre":[116],"counterexample.":[117]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}
