{"id":"https://openalex.org/W3034356521","doi":"https://doi.org/10.1137/19m1264060","title":"Alternative Reduction by Stages of Keplerian Systems. Positive, Negative, and Zero Energy","display_name":"Alternative Reduction by Stages of Keplerian Systems. Positive, Negative, and Zero Energy","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3034356521","doi":"https://doi.org/10.1137/19m1264060","mag":"3034356521"},"language":"en","primary_location":{"id":"doi:10.1137/19m1264060","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1264060","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037292181","display_name":"Francisco Crespo","orcid":"https://orcid.org/0000-0002-5930-8523"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Francisco Crespo","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5930-8523","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103258284","display_name":"S. Ferrer","orcid":"https://orcid.org/0000-0003-0084-0192"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sebasti\u00e1n Ferrer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2662,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61359448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"19","issue":"2","first_page":"1525","last_page":"1539"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T10325","display_name":"Astro and Planetary Science","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6569142937660217},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6149948239326477},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.5557318925857544},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5305899381637573},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.508623480796814},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.49492162466049194},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4927223026752472},{"id":"https://openalex.org/keywords/kepler-problem","display_name":"Kepler problem","score":0.48615118861198425},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4814735949039459},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4528560936450958},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4241466522216797},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.30059516429901123},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.29883456230163574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12716150283813477}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6569142937660217},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6149948239326477},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5557318925857544},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5305899381637573},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.508623480796814},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.49492162466049194},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4927223026752472},{"id":"https://openalex.org/C20422478","wikidata":"https://www.wikidata.org/wiki/Q2564682","display_name":"Kepler problem","level":2,"score":0.48615118861198425},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4814735949039459},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4528560936450958},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4241466522216797},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.30059516429901123},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29883456230163574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12716150283813477},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1264060","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1264060","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1258113213","display_name":null,"funder_award_id":"MTM2015-64095-P","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G5100123879","display_name":null,"funder_award_id":"11160224","funder_id":"https://openalex.org/F4320338073","funder_display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico"},{"id":"https://openalex.org/G7339443911","display_name":null,"funder_award_id":"ESP2017-331 87271-P","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320338073","display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","ror":"https://ror.org/02ap3w078"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1493815990","https://openalex.org/W1971087407","https://openalex.org/W2003059336","https://openalex.org/W2021496542","https://openalex.org/W2036946102","https://openalex.org/W2066734941","https://openalex.org/W2068501923","https://openalex.org/W2132701859","https://openalex.org/W2154821573","https://openalex.org/W2963991355"],"related_works":["https://openalex.org/W2088203660","https://openalex.org/W1617748564","https://openalex.org/W3013085049","https://openalex.org/W3022939440","https://openalex.org/W2110143569","https://openalex.org/W3122938442","https://openalex.org/W1560496689","https://openalex.org/W4303022582","https://openalex.org/W4386900933","https://openalex.org/W4385301946"],"abstract_inverted_index":{"This":[0,43],"work":[1],"deals":[2],"with":[3],"the":[4,8,20,25,46,50,54,96,103,111,118,130,136,140],"full":[5],"reduction":[6,66],"of":[7,49,72,84,106,120,139],"spatial":[9],"Kepler":[10,26],"system":[11,27],"for":[12,60],"bounded":[13],"and":[14,28,53,123,144],"unbounded":[15],"motions.":[16],"Precisely,":[17],"we":[18,133],"consider":[19],"four-dimensional":[21],"oscillator":[22],"associated":[23],"to":[24,89],"carry":[29],"out":[30],"our":[31],"program":[32],"in":[33,155],"three":[34],"stages:":[35],"axial-axial-energy":[36],"rather":[37],"than":[38],"energy-axial-axial":[39],"as":[40,117,126],"is":[41,80,100,115],"customary.":[42],"approach":[44],"reveals":[45],"true":[47],"role":[48],"$\\mathcal{KS}$":[51],"map":[52,105],"bilinear":[55,98],"relation.":[56],"Our":[57],"development":[58],"allows":[59],"a":[61,69,90,107],"global":[62],"analysis":[63],"at":[64],"each":[65,73],"stage":[67],"providing":[68],"complete":[70],"description":[71],"reduced":[74,78,113,150],"space.":[75],"The":[76,142],"first":[77],"space":[79,114],"described":[81,154],"by":[82,102],"means":[83],"only":[85],"six":[86],"invariants":[87],"leading":[88],"nonsingular":[91],"six-dimensional":[92],"Poisson":[93],"manifold.":[94],"Then,":[95],"classical":[97],"relation":[99],"replaced":[101],"momentum":[104],"geometric":[108],"reduction.":[109],"Furthermore,":[110],"second":[112],"given":[116],"product":[119],"two":[121],"hyperboloids":[122],"has":[124],"cones":[125],"singular":[127],"strata.":[128],"For":[129],"last":[131],"stage,":[132],"distinguish":[134],"among":[135],"possible":[137],"sign":[138],"energy.":[141],"positive":[143],"zero":[145],"cases":[146],"bring":[147],"new":[148],"noncompact":[149],"spaces":[151],"which":[152],"are":[153],"detail.":[156]},"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
