{"id":"https://openalex.org/W2792892743","doi":"https://doi.org/10.1007/s10817-017-9448-y","title":"A Verified ODE Solver and the Lorenz Attractor","display_name":"A Verified ODE Solver and the Lorenz Attractor","publication_year":2018,"publication_date":"2018-01-22","ids":{"openalex":"https://openalex.org/W2792892743","doi":"https://doi.org/10.1007/s10817-017-9448-y","mag":"2792892743","pmid":"https://pubmed.ncbi.nlm.nih.gov/30069071"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-017-9448-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-017-9448-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10817-017-9448-y.pdf","source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10817-017-9448-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089633378","display_name":"Fabian Immler","orcid":"https://orcid.org/0000-0002-5468-1513"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Fabian Immler","raw_affiliation_strings":["Institut f\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen, Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0002-5468-1513","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Technische Universit\u00e4t M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089633378"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.9344,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.87424925,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"61","issue":"1-4","first_page":"73","last_page":"111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.7792506217956543},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.6891307234764099},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6760799884796143},{"id":"https://openalex.org/keywords/hol","display_name":"HOL","score":0.6667947769165039},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6325379610061646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4993021488189697},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.4852900207042694},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.48351600766181946},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.46650785207748413},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.4372403025627136},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3994938135147095},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3913643956184387},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38485753536224365},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33963894844055176},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.33656802773475647},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3331061005592346},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.22125470638275146},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1584688127040863},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0834275484085083}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7792506217956543},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.6891307234764099},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6760799884796143},{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.6667947769165039},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6325379610061646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4993021488189697},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.4852900207042694},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.48351600766181946},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.46650785207748413},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.4372403025627136},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3994938135147095},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3913643956184387},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38485753536224365},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33963894844055176},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.33656802773475647},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3331061005592346},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.22125470638275146},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1584688127040863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0834275484085083},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10817-017-9448-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-017-9448-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10817-017-9448-y.pdf","source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},{"id":"pmid:30069071","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30069071","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of automated reasoning","raw_type":null},{"id":"pmh:oai:europepmc.org:5015321","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6044317","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"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":null,"raw_type":"Text"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1531200","is_oa":true,"landing_page_url":"http://mediatum.ub.tum.de/node?id=1531200","pdf_url":null,"source":{"id":"https://openalex.org/S4306400453","display_name":"mediaTUM \u2013 the media and publications repository of the Technical University Munich (Technical University Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10817-017-9448-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-017-9448-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10817-017-9448-y.pdf","source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1632707047","display_name":null,"funder_award_id":"RTG 1480","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G653283282","display_name":null,"funder_award_id":"NI 491/16-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2792892743.pdf","grobid_xml":"https://content.openalex.org/works/W2792892743.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W1713610","https://openalex.org/W56092462","https://openalex.org/W69146909","https://openalex.org/W101424827","https://openalex.org/W622938260","https://openalex.org/W970850559","https://openalex.org/W1016224041","https://openalex.org/W1480808529","https://openalex.org/W1482491673","https://openalex.org/W1511826042","https://openalex.org/W1545409775","https://openalex.org/W1546282418","https://openalex.org/W1578750710","https://openalex.org/W1589876408","https://openalex.org/W1606342649","https://openalex.org/W1683154758","https://openalex.org/W1915348541","https://openalex.org/W1924092145","https://openalex.org/W1989097268","https://openalex.org/W2006731094","https://openalex.org/W2019398782","https://openalex.org/W2044413922","https://openalex.org/W2051724490","https://openalex.org/W2058099048","https://openalex.org/W2066621462","https://openalex.org/W2106192381","https://openalex.org/W2121020818","https://openalex.org/W2131798279","https://openalex.org/W2141394518","https://openalex.org/W2146104088","https://openalex.org/W2147177731","https://openalex.org/W2157264766","https://openalex.org/W2166210250","https://openalex.org/W2168254994","https://openalex.org/W2174838357","https://openalex.org/W2206900256","https://openalex.org/W2304289376","https://openalex.org/W2395675371","https://openalex.org/W2483648716","https://openalex.org/W2549584611","https://openalex.org/W2793741686","https://openalex.org/W2797934247","https://openalex.org/W3004618708","https://openalex.org/W3100674527","https://openalex.org/W3217753397","https://openalex.org/W4231102510","https://openalex.org/W4235282062","https://openalex.org/W4250846042","https://openalex.org/W4285719527","https://openalex.org/W4292994524"],"related_works":["https://openalex.org/W4289542543","https://openalex.org/W2891065597","https://openalex.org/W1509796342","https://openalex.org/W1742246664","https://openalex.org/W3158046166","https://openalex.org/W2033042940","https://openalex.org/W2089902280","https://openalex.org/W2145782975","https://openalex.org/W2810701175","https://openalex.org/W3037847165"],"abstract_inverted_index":{"A":[0],"rigorous":[1],"numerical":[2],"algorithm,":[3],"formally":[4],"verified":[5],"with":[6],"Isabelle/HOL,":[7],"is":[8,26,67],"used":[9,16],"to":[10,17],"certify":[11],"the":[12,21],"computations":[13],"that":[14,86],"Tucker":[15],"prove":[18],"chaos":[19],"for":[20],"Lorenz":[22],"attractor.":[23],"The":[24,78],"verification":[25],"based":[27,54],"on":[28,55,90],"a":[29,32,62],"formalization":[30],"of":[31,35],"diverse":[33],"variety":[34],"mathematics":[36,40],"and":[37,45,58,72,76],"algorithms.":[38],"Formalized":[39],"include":[41,49],"ordinary":[42],"differential":[43],"equations":[44],"Poincar\u00e9":[46],"maps.":[47],"Algorithms":[48],"low":[50],"level":[51],"approximation":[52],"schemes":[53],"Runge-Kutta":[56],"methods":[57],"affine":[59],"arithmetic.":[60],"On":[61],"high":[63],"level,":[64],"reachability":[65],"analysis":[66],"guided":[68],"by":[69],"static":[70],"hybridization":[71],"adaptive":[73],"step-size":[74],"control":[75],"splitting.":[77],"algorithms":[79],"are":[80],"systematically":[81],"refined":[82],"towards":[83],"an":[84],"implementation":[85],"can":[87],"be":[88],"executed":[89],"Tucker's":[91],"original":[92],"input":[93],"data.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-23T08:51:43.019350","created_date":"2025-10-10T00:00:00"}
