{"id":"https://openalex.org/W7214568651","doi":"https://doi.org/10.48550/arxiv.2609.30821","title":"Bounding extreme events in dynamical systems over an infinite time horizon","display_name":"Bounding extreme events in dynamical systems over an infinite time horizon","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214568651","doi":"https://doi.org/10.48550/arxiv.2609.30821"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30821","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30821","pdf_url":"https://arxiv.org/pdf/2609.30821","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/2609.30821","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5117630115","display_name":"Karol\u00edna Sehnalov\u00e1","orcid":"https://orcid.org/0009-0008-3282-6276","observed_orcids":["https://orcid.org/0009-0008-3282-6276"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sehnalov\u00e1, Karol\\'\u0131na","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024399660","display_name":"Milan Korda","orcid":"https://orcid.org/0000-0002-5755-8326","observed_orcids":["https://orcid.org/0000-0002-5755-8326"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Korda, Milan","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":null,"has_fulltext":true,"cited_by_count":1,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.5702999830245972,"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":0.5702999830245972,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.05490000173449516,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.04410000145435333,"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/extreme-events","display_name":"extreme events","score":0.8500000238418579},{"id":"https://openalex.org/keywords/dynamical-systems","display_name":"dynamical systems","score":0.796999990940094},{"id":"https://openalex.org/keywords/infinite-horizon","display_name":"infinite horizon","score":0.9850000143051147},{"id":"https://openalex.org/keywords/occupation-measures","display_name":"occupation measures","score":0.7850000262260437},{"id":"https://openalex.org/keywords/liouville-equation","display_name":"Liouville equation","score":0.9190000295639038},{"id":"https://openalex.org/keywords/reachability-problem","display_name":"reachability problem","score":0.7170000076293945},{"id":"https://openalex.org/keywords/level-sets","display_name":"level sets","score":0.6100000143051147},{"id":"https://openalex.org/keywords/superposition","display_name":"superposition","score":0.859000027179718},{"id":"https://openalex.org/keywords/trajectory-ensembles","display_name":"trajectory ensembles","score":0.5849999785423279}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7081000208854675},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5001000165939331},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.4587000012397766},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.45509999990463257},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4535999894142151},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.43309998512268066},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.39989998936653137},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.39910000562667847},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.39820000529289246},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.3944999873638153},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3691999912261963},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.34769999980926514},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3427000045776367},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3377000093460083},{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.32899999618530273},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.3086000084877014},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C175197506","wikidata":"https://www.wikidata.org/wiki/Q1003225","display_name":"Measure-preserving dynamical system","level":5,"score":0.2922999858856201},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2759999930858612},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2556000053882599}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.30821","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30821","pdf_url":"https://arxiv.org/pdf/2609.30821","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":"pmh:oai:HAL:hal-05761573v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05761573v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.30821","doi":"https://doi.org/10.48550/arxiv.2609.30821","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30821","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","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":"pmh:oai:arXiv.org:2609.30821","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30821","pdf_url":"https://arxiv.org/pdf/2609.30821","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":[{"id":"https://openalex.org/F4320309972","display_name":"\u010cesk\u00e9 Vysok\u00e9 U\u010den\u00ed Technick\u00e9 v Praze","ror":"https://ror.org/03kqpb082"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214568651.pdf","grobid_xml":"https://content.openalex.org/works/W7214568651.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2973182962","https://openalex.org/W2898168308","https://openalex.org/W2419083510","https://openalex.org/W7134042068","https://openalex.org/W2151754075","https://openalex.org/W2144315318","https://openalex.org/W2105827181","https://openalex.org/W1669672717","https://openalex.org/W3103366751","https://openalex.org/W2152195867"],"abstract_inverted_index":{"This":[0,116,178],"work":[1],"addresses":[2],"the":[3,62,68,71,75,83,87,104,130,149,160,182,200],"computation":[4],"of":[5,8,12,74,103,120,142,148,187],"extreme":[6,64],"values":[7,34,65,135],"observables":[9],"along":[10],"trajectories":[11,25,192],"dynamical":[13],"systems":[14],"over":[15],"an":[16,169],"\\ks{infinite":[17],"time":[18,38,84],"horizon}.":[19],"The":[20,49,77],"setting":[21],"is":[22,80,90],"intrinsically":[23],"global:":[24],"may":[26],"exhibit":[27],"large":[28],"transient":[29,69],"excursions,":[30],"approach":[31],"their":[32],"largest":[33],"only":[35],"asymptotically":[36],"as":[37],"tends":[39],"to":[40,44,92],"infinity,":[41],"or":[42],"escape":[43],"infinity":[45],"in":[46,56],"finite":[47],"time.":[48],"proposed":[50],"framework":[51],"treats":[52],"these":[53],"\\mk{":[54],"scenarios}":[55],"a":[57,100,108,118,140,156,165,174],"unified":[58],"way,":[59],"so":[60],"that":[61,81,181],"resulting":[63],"reflect":[66],"both":[67],"and":[70,112,129,196,202],"asymptotic":[72],"behavior":[73],"dynamics.":[76],"main":[78],"difficulty":[79],"neither":[82],"interval":[85],"nor":[86],"state":[88,105],"space":[89,106],"assumed":[91],"be":[93,153],"compact.":[94],"We":[95],"address":[96],"this":[97],"by":[98,155],"combining":[99],"radial":[101],"compactification":[102],"with":[107,173],"compactified":[109],"clock":[110],"variable":[111],"discounted":[113],"occupation":[114,127],"measures.":[115],"yields":[117],"description":[119],"trajectory":[121],"ensembles":[122,186],"on":[123],"compact":[124],"sets":[125,147],"via":[126],"measures":[128],"associated":[131],"Liouville's":[132,171],"equation.":[133],"Extreme":[134],"are":[136],"then":[137],"characterized":[138],"through":[139],"family":[141],"reachability":[143],"problems":[144],"for":[145,168],"level":[146],"observable,":[150],"which":[151],"can":[152],"solved":[154],"bisection":[157],"procedure.":[158],"On":[159],"theoretical":[161],"side,":[162],"we":[163],"prove":[164],"superposition":[166],"principle":[167],"infinite-horizon":[170],"equation":[172],"time-distributed":[175],"terminal":[176],"measure.":[177],"result":[179],"shows":[180],"measure":[183],"formulation":[184],"represents":[185],"stopped":[188],"admissible":[189],"trajectories,":[190],"including":[191],"\\ks{that":[193],"never":[194],"stop},":[195],"establishes":[197],"equivalence":[198],"between":[199],"trajectory-level":[201],"measure-level":[203],"descriptions.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-28T00:00:00"}
