{"id":"https://openalex.org/W7225572736","doi":"https://doi.org/10.5281/zenodo.24054556","title":"An Exactly Soluble Three-Dimensional Toy Model with a Saddle Separatrix","display_name":"An Exactly Soluble Three-Dimensional Toy Model with a Saddle Separatrix","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225572736","doi":"https://doi.org/10.5281/zenodo.24054556"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24054556","doi":"https://doi.org/10.5281/zenodo.24054556","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054556","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24054556","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161102684","display_name":"Jonah schloss","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Schloss, Jonah","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161102684"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"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":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.6699000000953674,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.6699000000953674,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.1770000010728836,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.05180000141263008,"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/analytical-solution","display_name":"analytical solution","score":0.9380000233650208},{"id":"https://openalex.org/keywords/hyperbolic-saddles","display_name":"hyperbolic saddles","score":0.9520000219345093},{"id":"https://openalex.org/keywords/stable-manifolds","display_name":"stable manifolds","score":0.8019999861717224},{"id":"https://openalex.org/keywords/invariant-plane","display_name":"invariant plane","score":0.8320000171661377},{"id":"https://openalex.org/keywords/basins-of-attraction","display_name":"basins of attraction","score":0.9779999852180481},{"id":"https://openalex.org/keywords/hydrodynamic-stability","display_name":"hydrodynamic stability","score":0.9929999709129333},{"id":"https://openalex.org/keywords/exponential-bounds","display_name":"exponential bounds","score":0.6510000228881836},{"id":"https://openalex.org/keywords/three-dimensional-dynamical-systems","display_name":"three-dimensional dynamical systems","score":0.5989999771118164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6236000061035156},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.5770999789237976},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5527999997138977},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5254999995231628},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5110999941825867},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4887999892234802},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.48750001192092896},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4803999960422516},{"id":"https://openalex.org/C76379757","wikidata":"https://www.wikidata.org/wiki/Q2902561","display_name":"Separatrix","level":3,"score":0.47909998893737793},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.4641000032424927},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.45980000495910645},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.4595000147819519},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.45829999446868896},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.43639999628067017},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.4320000112056732},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4214000105857849},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4194999933242798},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.3993000090122223},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.3693999946117401},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.3481000065803528},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30959999561309814},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30709999799728394},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.29010000824928284},{"id":"https://openalex.org/C9628104","wikidata":"https://www.wikidata.org/wiki/Q788009","display_name":"Autonomous system (mathematics)","level":2,"score":0.2870999872684479},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.2736000120639801},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C2778671503","wikidata":"https://www.wikidata.org/wiki/Q7542110","display_name":"Slow manifold","level":3,"score":0.2669999897480011},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.25589999556541443}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24054556","doi":"https://doi.org/10.5281/zenodo.24054556","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054556","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"article-journal"},{"id":"doi:10.5281/zenodo.24054557","doi":"https://doi.org/10.5281/zenodo.24054557","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054557","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24054556","doi":"https://doi.org/10.5281/zenodo.24054556","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054556","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"article-journal"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2568485391","https://openalex.org/W7153596670","https://openalex.org/W3169079210","https://openalex.org/W7037516918","https://openalex.org/W2997397937","https://openalex.org/W3193752041","https://openalex.org/W4283019980","https://openalex.org/W3123075579","https://openalex.org/W4234691186","https://openalex.org/W2990686327"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,28,60,69],"three-dimensional":[3],"autonomous":[4],"ODE":[5],"system":[6,26,62],"that":[7,39],"admits":[8],"an":[9,36],"exact":[10],"closed-form":[11],"solution":[12],"in":[13,21,76],"its":[14],"transition":[15],"coordinate":[16],"and":[17,89],"explicit":[18],"exponential":[19],"bounds":[20],"the":[22,41,55,86,93],"transverse":[23],"coordinates.":[24],"The":[25,49,79],"possesses":[27],"hyperbolic":[29],"saddle":[30],"whose":[31,63],"two-dimensional":[32],"stable":[33],"manifold":[34],"is":[35,51,59,66,99],"invariant":[37],"plane":[38],"separates":[40],"phase":[42],"space":[43],"into":[44],"two":[45],"basins":[46],"of":[47,92],"attraction.":[48],"model":[50],"not":[52],"derived":[53],"from":[54],"Navier-Stokes":[56],"equations.":[57],"It":[58],"toy":[61],"only":[64],"purpose":[65],"to":[67,84],"provide":[68],"trivially":[70],"verifiable":[71],"benchmark":[72],"for":[73],"edge-tracking":[74],"algorithms":[75],"hydrodynamic":[77],"stability.":[78],"saddle's":[80],"eigenvalues":[81],"are":[82],"chosen":[83],"match":[85],"logarithmic":[87],"contraction":[88],"expansion":[90],"rates":[91],"Jonah":[94],"triangle.":[95],"This":[96],"parameter":[97],"choice":[98],"noted":[100],"but":[101],"carries":[102],"no":[103],"dynamical":[104],"derivation.":[105]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}