{"id":"https://openalex.org/W7225638807","doi":"https://doi.org/10.5281/zenodo.24081855","title":"The Characteristic Polynomial of the Jonah Saddle","display_name":"The Characteristic Polynomial of the Jonah Saddle","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225638807","doi":"https://doi.org/10.5281/zenodo.24081855"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24081855","doi":"https://doi.org/10.5281/zenodo.24081855","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24081855","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.24081855","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161293852","display_name":"Schloss Jonah","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/A5161293852"],"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":0.95169997215271,"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":0.95169997215271,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.03420000150799751,"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/T12504","display_name":"Mathematics and Applications","score":0.004000000189989805,"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/characteristic-polynomial","display_name":"characteristic polynomial","score":0.7360000014305115},{"id":"https://openalex.org/keywords/jacobian-determinant","display_name":"Jacobian determinant","score":0.7910000085830688},{"id":"https://openalex.org/keywords/linearization","display_name":"linearization","score":0.39399999380111694},{"id":"https://openalex.org/keywords/two-dimensional-maps","display_name":"two-dimensional maps","score":0.49300000071525574},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"saddle-node bifurcation","score":0.3869999945163727}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8475000262260437},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6601999998092651},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.593500018119812},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4765999913215637},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4690999984741211},{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3833000063896179},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.3668999969959259},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.35530000925064087},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32109999656677246},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.2655999958515167}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24081855","doi":"https://doi.org/10.5281/zenodo.24081855","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24081855","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.24081856","doi":"https://doi.org/10.5281/zenodo.24081856","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24081856","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.24081855","doi":"https://doi.org/10.5281/zenodo.24081855","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24081855","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225619584","https://openalex.org/W7225654282","https://openalex.org/W7225642184","https://openalex.org/W7225642796","https://openalex.org/W7225627302","https://openalex.org/W7225591994","https://openalex.org/W7225597323","https://openalex.org/W2018843163","https://openalex.org/W7225584248","https://openalex.org/W1536615012"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,6,11,15,27,34,42,51,77,83,88,95,106,121,125,131,138,146,151,158,169,184,200,204,211,224,227],"two-dimensional":[3,228],"linearisation":[4,89],"of":[5,80,134,154,226,233],"pedal":[7,147],"shape":[8],"map":[9,133,148,153,186,229],"at":[10,74,124,230],"Jonah":[12,126,159],"saddle,":[13],"using":[14],"longitudinal":[16],"and":[17,22,50,87,203],"transverse":[18,84],"multipliers":[19],"lambda":[20,23,46,48,59,62,218],"u(t)":[21],"s(t)":[24],"imported":[25,212],"from":[26],"companion":[28],"papers.":[29],"From":[30],"them":[31],"we":[32],"derive":[33],"trace":[35],"T(t)=(3t":[36],"minus":[37,39,55,61,98],"1)(2t":[38],"1)/t":[40],"squared,":[41,64],"determinant":[43,71,96,123],"Delta":[44,57],"(t)=":[45],"u":[47,60],"s,":[49],"discriminant":[52],"T":[53],"squared":[54,100],"4":[56],"=(":[58],"s)":[63],"which":[65],"is":[66,97,112,128,149,179,196,220],"positive":[67,143],"on":[68,210],"(1/2,1).":[69],"The":[70,108,215],"changes":[72],"sign":[73],"t":[75,117,165,192],"0=(3+":[76],"square":[78],"root":[79],"3)/6,":[81],"where":[82],"multiplier":[85,213],"vanishes":[86],"has":[90,141],"rank":[91],"one.":[92],"At":[93],"t=7/10":[94],"11":[99],"times":[101,103],"13":[102],"41/7":[104],"to":[105,137],"6.":[107],"main":[109],"new":[110],"result":[111],"a":[113,155,173,189],"Liouville":[114,205],"obstruction.":[115,182],"For":[116,164],"in":[118,161,166,188,193],"(1/2,t":[119],"0],":[120],"Jacobian":[122,225],"point":[127,160],"non-positive,":[129],"whereas":[130],"time-T":[132,152],"any":[135],"C":[136],"1":[139],"flow":[140,156,175,190],"strictly":[142],"determinant.":[144],"Hence":[145],"not":[150,235],"near":[157],"this":[162],"range.":[163],"(t":[167,194],"0,1)":[168,195],"linear":[170,181],"part":[171],"admits":[172],"real":[174],"logarithm,":[176],"so":[177],"there":[178],"no":[180],"Whether":[183],"nonlinear":[185],"embeds":[187],"for":[191,217],"left":[197],"open.":[198],"Status:":[199],"algebraic":[201],"identities":[202],"argument":[206],"are":[207],"proved,":[208],"conditional":[209],"formulas.":[214],"formula":[216],"s":[219],"checked":[221],"numerically":[222],"against":[223],"eight":[231],"values":[232],"t,":[234],"proved":[236],"here.":[237]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}