{"id":"https://openalex.org/W2106428635","doi":"https://doi.org/10.1103/physrevlett.79.1018","title":"Lyapunov Exponents, Singularities, and a Riddling Bifurcation","display_name":"Lyapunov Exponents, Singularities, and a Riddling Bifurcation","publication_year":1997,"publication_date":"1997-08-11","ids":{"openalex":"https://openalex.org/W2106428635","doi":"https://doi.org/10.1103/physrevlett.79.1018","mag":"2106428635"},"language":"en","primary_location":{"id":"doi:10.1103/physrevlett.79.1018","doi":"https://doi.org/10.1103/physrevlett.79.1018","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevlett.79.1018","pdf_url":null,"source":{"id":"https://openalex.org/S24807848","display_name":"Physical Review Letters","issn_l":"0031-9007","issn":["0031-9007","1079-7114","1092-0145"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Letters","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2106428635"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5060832073","display_name":"Lora Billings B","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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lora Billings","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086402543","display_name":"James H. Curry","orcid":"https://orcid.org/0000-0003-4204-5250","observed_orcids":["https://orcid.org/0000-0003-4204-5250"]},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James H. Curry","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060331278","display_name":"Eric Phipps","orcid":"https://orcid.org/0000-0002-9118-4735","observed_orcids":["https://orcid.org/0000-0002-9118-4735"]},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Phipps","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":{"value":3750,"currency":"USD","value_usd":3750},"apc_paid":null,"fwci":3.6258,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.92030269,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"79","issue":"6","first_page":"1018","last_page":"1021"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9976000189781189,"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":0.9976000189781189,"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/T10244","display_name":"Chaos control and synchronization","score":0.00139999995008111,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-exponents","display_name":"Lyapunov exponents","score":0.9869999885559082},{"id":"https://openalex.org/keywords/non-invertible-maps","display_name":"non-invertible maps","score":0.7590000033378601},{"id":"https://openalex.org/keywords/planar-maps","display_name":"planar maps","score":0.6790000200271606},{"id":"https://openalex.org/keywords/singularities","display_name":"singularities","score":0.6610000133514404}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.8529232740402222},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.7496855854988098},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6865960359573364},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6021285057067871},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5943774580955505},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5608425140380859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5467197299003601},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40782272815704346},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4060762822628021},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3885883688926697},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22852835059165955},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.1714349091053009},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10838127136230469},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07235980033874512},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1103/physrevlett.79.1018","doi":"https://doi.org/10.1103/physrevlett.79.1018","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevlett.79.1018","pdf_url":null,"source":{"id":"https://openalex.org/S24807848","display_name":"Physical Review Letters","issn_l":"0031-9007","issn":["0031-9007","1079-7114","1092-0145"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Letters","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.46.7167","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.7167","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.udel.edu/~billings/cv/./riddle.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1969458001","https://openalex.org/W1971547656","https://openalex.org/W1971817931","https://openalex.org/W1983918081","https://openalex.org/W2119161220","https://openalex.org/W2138076202","https://openalex.org/W2168581605","https://openalex.org/W4298860934"],"related_works":["https://openalex.org/W4256560209","https://openalex.org/W7098881606","https://openalex.org/W2567701465","https://openalex.org/W2540795173","https://openalex.org/W2034837097","https://openalex.org/W7101028998","https://openalex.org/W2620374416","https://openalex.org/W2272789534","https://openalex.org/W3033758298","https://openalex.org/W2363110465"],"abstract_inverted_index":{"There":[0],"are":[1,50],"few":[2],"examples":[3],"in":[4],"dynamical":[5],"systems":[6],"theory":[7],"which":[8,26,47],"lend":[9],"themselves":[10],"to":[11,70],"exact":[12],"computations":[13,49],"of":[14,17,31,40,43,60,75],"macroscopic":[15],"variables":[16],"interest.":[18],"One":[19],"such":[20,48],"variable":[21],"is":[22],"the":[23,28,44,58],"Lyapunov":[24],"exponent":[25],"measures":[27],"average":[29],"attraction":[30],"an":[32,66],"invariant":[33,68],"set.":[34],"This":[35,52],"article":[36],"presents":[37],"a":[38,72],"family":[39],"noninvertible":[41],"transformations":[42],"plane":[45],"for":[46,65],"possible.":[51],"model":[53],"sheds":[54],"additional":[55],"insight":[56],"into":[57],"notion":[59],"what":[61],"it":[62],"can":[63],"mean":[64],"attracting":[67],"set":[69],"have":[71],"riddled":[73],"basin":[74],"attraction.":[76]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}