{"id":"https://openalex.org/W7082002700","doi":"https://doi.org/10.5281/zenodo.17137536","title":"On the Non-Structural Nature of Chaos in the Three-Body Problem","display_name":"On the Non-Structural Nature of Chaos in the Three-Body Problem","publication_year":2025,"publication_date":"2025-09-16","ids":{"openalex":"https://openalex.org/W7082002700","doi":"https://doi.org/10.5281/zenodo.17137536"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.17137536","doi":"https://doi.org/10.5281/zenodo.17137536","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.17137536","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","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.17137536","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"ALFREDO LUIS, ACOSTA PADILLA","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"ALFREDO LUIS, ACOSTA PADILLA","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.51962193,"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":true,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.6890000104904175,"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":0.6890000104904175,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.11069999635219574,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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":0.052799999713897705,"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/three-body-problem","display_name":"three-body problem","score":0.9980000257492065},{"id":"https://openalex.org/keywords/chaos","display_name":"chaos","score":0.6899999976158142},{"id":"https://openalex.org/keywords/modified-hamiltonian","display_name":"modified Hamiltonian","score":0.7570000290870667},{"id":"https://openalex.org/keywords/harmonic-confinement","display_name":"harmonic confinement","score":0.8019999861717224},{"id":"https://openalex.org/keywords/global-stability","display_name":"global stability","score":0.800000011920929},{"id":"https://openalex.org/keywords/kam-theory","display_name":"KAM theory","score":0.9079999923706055},{"id":"https://openalex.org/keywords/nekhoroshev-stability","display_name":"Nekhoroshev stability","score":0.9020000100135803},{"id":"https://openalex.org/keywords/relative-equilibria","display_name":"relative equilibria","score":0.8450000286102295},{"id":"https://openalex.org/keywords/lagrange-points","display_name":"Lagrange points","score":0.9909999966621399},{"id":"https://openalex.org/keywords/integrability","display_name":"integrability","score":0.6610000133514404},{"id":"https://openalex.org/keywords/sun-earth-moon-system","display_name":"Sun-Earth-Moon system","score":0.8220000267028809},{"id":"https://openalex.org/keywords/celestial-mechanics","display_name":"celestial mechanics","score":0.8899999856948853}],"concepts":[{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6261000037193298},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6241999864578247},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5911999940872192},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5644000172615051},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5410000085830688},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.423799991607666},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.40720000863075256},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.35839998722076416},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33000001311302185},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.32199999690055847},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3084999918937683},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.2930000126361847},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27399998903274536},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2623000144958496},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.25290000438690186},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.17137536","doi":"https://doi.org/10.5281/zenodo.17137536","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.17137536","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":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.17137537","doi":"https://doi.org/10.5281/zenodo.17137537","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.17137537","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":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.17137536","doi":"https://doi.org/10.5281/zenodo.17137536","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.17137536","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,155,171],"work":[1],"presents":[2],"a":[3,30,43,78,194],"theoretical":[4],"framework":[5],"to":[6,63,72,137,149,158,198],"stabilize":[7],"the":[8,14,18,33,37,74,100,106,114,134,139,151,165,183,199],"three-body":[9],"problem.":[10],"It":[11,128],"demonstrates":[12],"that":[13,48,98,131],"chaos":[15,179],"associated":[16],"with":[17],"classical":[19],"Newtonian":[20],"model":[21],"is":[22,46,49,96,117,129,190],"not":[23],"an":[24,159,174],"inescapable":[25],"structural":[26],"property,":[27],"but":[28],"rather":[29],"consequence":[31],"of":[32,36,162,182,186,196],"mathematical":[34],"singularities":[35],"point-mass":[38],"model.":[39],"To":[40],"this":[41,104],"end,":[42],"modified":[44],"Hamiltonian":[45],"introduced":[47],"analytically":[50],"tractable":[51],"and":[52,66,87,108,119,168,189],"more":[53],"physically":[54],"realistic,":[55],"using":[56],"two":[57],"key":[58],"mechanisms:":[59],"A":[60,69],"Plummer":[61],"potential":[62],"regularize":[64],"collisions":[65],"eliminate":[67],"singularities.":[68],"harmonic":[70],"confinement":[71],"ensure":[73],"system's":[75,101,115],"stability":[76],"on":[77],"large":[79],"scale.":[80],"Main":[81],"Results:":[82],"Global":[83],"Stability:":[84],"An":[85],"explicit":[86],"constructive":[88],"threshold":[89],"(\u03b3":[90],"+":[91],"\u03a9\u00b2":[92],">":[93],"B(m,":[94],"\u03b5))":[95],"derived":[97],"guarantees":[99],"convexity.":[102],"Under":[103],"condition,":[105],"KAM":[107],"Nekhoroshev":[109],"theorems":[110],"become":[111],"applicable,":[112],"ensuring":[113],"behavior":[116],"stable":[118],"predictable":[120],"for":[121,177],"exponentially":[122],"long":[123],"times.":[124],"Exact":[125],"Local":[126],"Integrability:":[127],"shown":[130],"by":[132],"adjusting":[133],"model's":[135],"parameters":[136],"satisfy":[138],"Bertrand-Darboux":[140],"conditions":[141],"near":[142],"relative":[143],"equilibria":[144],"(Lagrange":[145],"points),":[146],"it's":[147],"possible":[148],"cancel":[150],"primary":[152],"chaotic":[153],"resonance.":[154],"gives":[156],"rise":[157],"additional":[160],"integral":[161],"motion,":[163],"making":[164],"system":[166],"exactly":[167],"locally":[169],"integrable.":[170],"approach":[172],"provides":[173],"analytical":[175],"solution":[176],"\"taming\"":[178],"in":[180],"one":[181],"fundamental":[184],"problems":[185],"celestial":[187],"mechanics":[188],"successfully":[191],"applied":[192],"as":[193],"proof":[195],"concept":[197],"Sun-Earth-Moon":[200],"system.":[201]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2025-10-10T00:00:00"}