{"id":"https://openalex.org/W7214056476","doi":"https://doi.org/10.48550/arxiv.2609.22800","title":"Jordan-Block Degeneracy and Cubic-Order Bifurcating Periodic Orbits in Minimum-Energy Optimal Control of Hamiltonian Equilibria","display_name":"Jordan-Block Degeneracy and Cubic-Order Bifurcating Periodic Orbits in Minimum-Energy Optimal Control of Hamiltonian Equilibria","publication_year":2026,"publication_date":"2026-09-19","ids":{"openalex":"https://openalex.org/W7214056476","doi":"https://doi.org/10.48550/arxiv.2609.22800"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.22800","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22800","pdf_url":"https://arxiv.org/pdf/2609.22800","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.22800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128120251","display_name":"Mai Bando","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bando, Mai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114187325","display_name":"Ayano Tsuruta","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]},{"id":"https://openalex.org/I2800865746","display_name":"Japan Aerospace Exploration Agency","ror":"https://ror.org/059yhyy33","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800865746"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tsuruta, Ayano","raw_affiliation_strings":["Department of Aeronautics and Astronautics , Kyushu University , 744 Motooka , Nishi-ku , Fukuoka , 819-0395 , Fukuoka , Japan","Human Spaceflight Technology Directorate , Japan Aerospace Exploration Agency (JAXA) , 2-1-1 Sengen , Tsukuba , 305-8505 , Ibaraki , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aeronautics and Astronautics , Kyushu University , 744 Motooka , Nishi-ku , Fukuoka , 819-0395 , Fukuoka , Japan","institution_ids":["https://openalex.org/I135598925"]},{"raw_affiliation_string":"Human Spaceflight Technology Directorate , Japan Aerospace Exploration Agency (JAXA) , 2-1-1 Sengen , Tsukuba , 305-8505 , Ibaraki , Japan","institution_ids":["https://openalex.org/I2800865746"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152469862","display_name":"Shanshan Pan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Pan, Shanshan","raw_affiliation_strings":["Department of Aeronautics and Astronautics , Kyushu University , 744 Motooka , Nishi-ku , Fukuoka , 819-0395 , Fukuoka , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aeronautics and Astronautics , Kyushu University , 744 Motooka , Nishi-ku , Fukuoka , 819-0395 , Fukuoka , Japan","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152466674","display_name":"Daniel J. Scheeres","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I2802236040","display_name":"University of Colorado System","ror":"https://ror.org/00jc20583","country_code":"US","type":"education","lineage":["https://openalex.org/I2802236040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scheeres, Daniel J.","raw_affiliation_strings":["Department of Aerospace Engineering Sciences , University of Colorado Boulder , Boulder , 80309 , Colorado , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering Sciences , University of Colorado Boulder , Boulder , 80309 , Colorado , USA","institution_ids":["https://openalex.org/I188538660","https://openalex.org/I2802236040"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.6439999938011169,"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"}},"topics":[{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.6439999938011169,"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":0.1932000070810318,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.09480000287294388,"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/periodic-orbits","display_name":"periodic orbits","score":0.8949999809265137},{"id":"https://openalex.org/keywords/pendulum","display_name":"pendulum","score":0.6119999885559082}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7067999839782715},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5562000274658203},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.544700026512146},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5023999810218811},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4731999933719635},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4296000003814697},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4027000069618225},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.37630000710487366},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.3553999960422516},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.30070000886917114},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2964000105857849},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.2897000014781952},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.26460000872612},{"id":"https://openalex.org/C152442685","wikidata":"https://www.wikidata.org/wiki/Q4286430","display_name":"Kapitza's pendulum","level":5,"score":0.263700008392334}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.22800","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22800","pdf_url":"https://arxiv.org/pdf/2609.22800","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.2609.22800","doi":"https://doi.org/10.48550/arxiv.2609.22800","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.22800","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.22800","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22800","pdf_url":"https://arxiv.org/pdf/2609.22800","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214056476.pdf","grobid_xml":"https://content.openalex.org/works/W7214056476.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1595765050","https://openalex.org/W1988244564","https://openalex.org/W2046826540","https://openalex.org/W2094085399","https://openalex.org/W2112507254","https://openalex.org/W2135305191","https://openalex.org/W2529725405","https://openalex.org/W2767578104","https://openalex.org/W4205482226","https://openalex.org/W4242360818","https://openalex.org/W4252504563","https://openalex.org/W4294553796","https://openalex.org/W4296477255","https://openalex.org/W4301747304","https://openalex.org/W4393213064","https://openalex.org/W4400322657","https://openalex.org/W7166310406","https://openalex.org/W7168025493"],"related_works":["https://openalex.org/W4393213064","https://openalex.org/W2047684597","https://openalex.org/W2038190837","https://openalex.org/W1149322295","https://openalex.org/W604709031","https://openalex.org/W7166310406","https://openalex.org/W2363747953","https://openalex.org/W1598653696","https://openalex.org/W1997472450","https://openalex.org/W1600801729"],"abstract_inverted_index":{"Equilibria":[0],"of":[1,14,97,113],"the":[2,15,34,43,87,93,103],"Hamiltonian":[3],"system":[4],"associated":[5],"with":[6,50],"Pontryagin's":[7],"minimum":[8],"principle":[9],"exhibit":[10],"an":[11,67,109],"exact":[12],"doubling":[13],"natural":[16],"spectrum":[17],"and,":[18],"under":[19],"a":[20,24,76],"simple":[21,29],"pairing":[22],"condition,":[23],"Jordan":[25],"block":[26],"at":[27,55,72],"every":[28],"purely":[30],"imaginary":[31],"eigenvalue.":[32],"Consequently,":[33],"classical":[35],"Lyapunov":[36],"Center":[37],"Theorem":[38],"does":[39],"not":[40],"apply":[41],"to":[42],"augmented":[44],"system,":[45],"and":[46,64,89],"no":[47],"periodic":[48,69,114],"orbit":[49],"nonzero":[51],"optimal":[52],"control":[53],"bifurcates":[54],"linear":[56],"order.":[57],"We":[58],"establish":[59],"this":[60],"mechanism":[61,80],"in":[62,75,83],"general":[63],"show":[65],"that":[66],"optimal-control-induced":[68],"family":[70,112],"emerges":[71],"cubic":[73],"order":[74],"Lindstedt--Poincar\u00e9":[77],"expansion.":[78],"The":[79],"is":[81,106],"illustrated":[82],"closed":[84],"form":[85],"for":[86,92],"pendulum":[88],"evaluated":[90],"numerically":[91],"planar":[94],"$L_2$":[95],"equilibrium":[96],"Hill's":[98],"restricted":[99],"three-body":[100],"problem,":[101],"where":[102],"third-order":[104],"approximation":[105],"validated":[107],"against":[108],"independently":[110],"computed":[111],"orbits.":[115]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}
