{"id":"https://openalex.org/W7225627462","doi":"https://doi.org/10.5281/zenodo.24066645","title":"Global Stability of a Nonlinear Self-Adjoint Operator Flow via a Tracial Lyapunov Functional","display_name":"Global Stability of a Nonlinear Self-Adjoint Operator Flow via a Tracial Lyapunov Functional","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225627462","doi":"https://doi.org/10.5281/zenodo.24066645"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24066645","doi":"https://doi.org/10.5281/zenodo.24066645","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24066645","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":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24066645","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161330558","display_name":"alejandro cruz morales","orcid":"https://orcid.org/0009-0002-4285-113X","observed_orcids":["https://orcid.org/0009-0002-4285-113X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"cruz morales, alejandro","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0002-4285-113X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161330558"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.4066999852657318,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.4066999852657318,"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"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.2583000063896179,"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"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.13539999723434448,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/self-adjoint-operators","display_name":"self-adjoint operators","score":0.8640000224113464},{"id":"https://openalex.org/keywords/nonlinear-flow","display_name":"nonlinear flow","score":0.6980000138282776},{"id":"https://openalex.org/keywords/lyapunov-functional","display_name":"Lyapunov functional","score":0.8989999890327454},{"id":"https://openalex.org/keywords/tracial-states","display_name":"tracial states","score":0.9319999814033508},{"id":"https://openalex.org/keywords/global-asymptotic-stability","display_name":"global asymptotic stability","score":0.8569999933242798},{"id":"https://openalex.org/keywords/cubic-damping","display_name":"cubic damping","score":0.7889999747276306},{"id":"https://openalex.org/keywords/power-law-decay","display_name":"power-law decay","score":0.7929999828338623},{"id":"https://openalex.org/keywords/noncommutativity","display_name":"non-commutativity","score":0.8330000042915344},{"id":"https://openalex.org/keywords/commutative-limit","display_name":"commutative limit","score":0.7310000061988831}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8165000081062317},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6509000062942505},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6157000064849854},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5486999750137329},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5315999984741211},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.49880000948905945},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.49300000071525574},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.489300012588501},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.45899999141693115},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4440999925136566},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42800000309944153},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4165000021457672},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.4074999988079071},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.37779998779296875},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3215000033378601},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2831000089645386},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.25850000977516174}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24066645","doi":"https://doi.org/10.5281/zenodo.24066645","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24066645","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":"Preprint"},{"id":"doi:10.5281/zenodo.24066646","doi":"https://doi.org/10.5281/zenodo.24066646","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24066646","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":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24066645","doi":"https://doi.org/10.5281/zenodo.24066645","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24066645","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":"Preprint"},"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/W1821546070","https://openalex.org/W3007811247","https://openalex.org/W3021029334","https://openalex.org/W2054714794","https://openalex.org/W2033878114","https://openalex.org/W1995162135","https://openalex.org/W2087402326","https://openalex.org/W2290790550","https://openalex.org/W4387777192","https://openalex.org/W2314124321"],"abstract_inverted_index":{"This":[0,51],"self-contained":[1],"note":[2,111],"explores":[3],"a":[4,11,20,29,35,82],"nonlinear":[5],"flow":[6],"on":[7],"self-adjoint":[8],"operators":[9],"within":[10],"Hilbert":[12],"space,":[13],"built":[14],"as":[15,60,62],"an":[16],"anticommutator-symmetrized":[17],"version":[18],"of":[19,56],"planar":[21],"rotator":[22],"with":[23],"isotropic":[24],"cubic":[25],"damping.":[26],"By":[27],"applying":[28],"faithful":[30],"tracial":[31],"state,":[32],"we":[33],"build":[34],"strict":[36],"Lyapunov":[37,54],"functional":[38],"whose":[39],"time":[40],"derivative":[41],"is":[42,73],"strictly":[43],"non-positive":[44],"and":[45,96,118],"only":[46],"vanishes":[47],"at":[48],"the":[49,53,57,70,78],"origin.":[50],"proves":[52],"stability":[55,65],"zero":[58],"equilibrium,":[59],"well":[61],"global":[63],"asymptotic":[64],"in":[66],"finite":[67],"dimensions.":[68],"Additionally,":[69],"commutative":[71,95],"limit":[72],"solved":[74],"exactly,":[75],"demonstrating":[76],"that":[77,100],"amplitude":[79],"decays":[80],"following":[81],"power-law":[83],"rate":[84],"rather":[85],"than":[86],"exponentially.":[87],"Numerical":[88],"tests":[89],"validate":[90],"these":[91],"results":[92],"for":[93],"both":[94],"non-commuting":[97],"cases,":[98],"proving":[99],"non-commutativity":[101],"does":[102],"not":[103],"speed":[104],"up":[105],"decay":[106],"into":[107],"exponential":[108],"behavior.":[109],"The":[110],"clearly":[112],"outlines":[113],"its":[114],"precise,":[115],"modest":[116],"scope":[117],"explicitly":[119],"separates":[120],"itself":[121],"from":[122],"older,":[123],"unverified":[124],"drafts.":[125]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}