{"id":"https://openalex.org/W3004981043","doi":"https://doi.org/10.1137/19m1268665","title":"Elliptic Bubbles in Moser's 4D Quadratic Map: The Quadfurcation","display_name":"Elliptic Bubbles in Moser's 4D Quadratic Map: The Quadfurcation","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3004981043","doi":"https://doi.org/10.1137/19m1268665","mag":"3004981043"},"language":"en","primary_location":{"id":"doi:10.1137/19m1268665","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1268665","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1807.06074","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Arnd B\u00e4cker","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arnd B\u00e4cker","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"James D. Meiss","orcid":"https://orcid.org/0000-0002-0019-0356"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"James D. Meiss","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0019-0356","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2671,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.50389009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"19","issue":"1","first_page":"442","last_page":"479"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.4790000021457672,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.4790000021457672,"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/T10244","display_name":"Chaos control and synchronization","score":0.17990000545978546,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.12219999730587006,"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/fixed-point","display_name":"Fixed point","score":0.7771999835968018},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7300999760627747},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5863999724388123},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5116999745368958},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4636000096797943},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.4323999881744385},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.36899998784065247},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.36890000104904175}],"concepts":[{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.7771999835968018},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7300999760627747},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6862000226974487},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5863999724388123},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5116999745368958},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4636000096797943},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40619999170303345},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.35899999737739563},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3465000092983246},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.3019999861717224},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.2720000147819519},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.26499998569488525},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.2567000091075897},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1268665","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1268665","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1807.06074","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.06074","pdf_url":"https://arxiv.org/pdf/1807.06074","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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:cuscholar:m900nv26t","is_oa":false,"landing_page_url":"https://scholar.colorado.edu/concern/articles/m900nv26t","pdf_url":null,"source":{"id":"https://openalex.org/S4306401957","display_name":"CU Scholar (University of Colorado Boulder)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I188538660","host_organization_name":"University of Colorado Boulder","host_organization_lineage":["https://openalex.org/I188538660"],"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":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1807.06074","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.06074","pdf_url":"https://arxiv.org/pdf/1807.06074","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[{"id":"https://openalex.org/G1108884084","display_name":null,"funder_award_id":"KE 537/6-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5969482202","display_name":null,"funder_award_id":"DMS-1440140","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G6058026567","display_name":null,"funder_award_id":"DMS-181248","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321613","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W12550025","https://openalex.org/W92074458","https://openalex.org/W1489032209","https://openalex.org/W1968312031","https://openalex.org/W1970820693","https://openalex.org/W1972724914","https://openalex.org/W1975377088","https://openalex.org/W1976860825","https://openalex.org/W1979245447","https://openalex.org/W1987765890","https://openalex.org/W1991100653","https://openalex.org/W2003315147","https://openalex.org/W2003695865","https://openalex.org/W2004863047","https://openalex.org/W2008896719","https://openalex.org/W2020679125","https://openalex.org/W2022745197","https://openalex.org/W2024973673","https://openalex.org/W2028403174","https://openalex.org/W2036236267","https://openalex.org/W2036770314","https://openalex.org/W2042768235","https://openalex.org/W2044105167","https://openalex.org/W2049293382","https://openalex.org/W2058132132","https://openalex.org/W2066760604","https://openalex.org/W2068742668","https://openalex.org/W2071986882","https://openalex.org/W2081461845","https://openalex.org/W2084643307","https://openalex.org/W2089640432","https://openalex.org/W2091671655","https://openalex.org/W2096030597","https://openalex.org/W2098550758","https://openalex.org/W2105623605","https://openalex.org/W2107292188","https://openalex.org/W2109486938","https://openalex.org/W2122946051","https://openalex.org/W2125566231","https://openalex.org/W2137151998","https://openalex.org/W2151358954","https://openalex.org/W2153020608","https://openalex.org/W2153218321","https://openalex.org/W2157773554","https://openalex.org/W2160163816","https://openalex.org/W2279693702","https://openalex.org/W2322377952","https://openalex.org/W2397215804","https://openalex.org/W2527537158","https://openalex.org/W2805032071","https://openalex.org/W2963925158"],"related_works":[],"abstract_inverted_index":{"Moser":[0],"derived":[1],"a":[2,26,49,60,65,73,89,114,179],"normal":[3],"form":[4],"for":[5,29],"the":[6,30,40,86,102,105,110,122,125,139,155,175],"family":[7,18,45],"of":[8,32,43,70,88,91,113,116,124,138,150,157,174,181],"four-dimensional":[9],"(4D),":[10],"quadratic,":[11],"symplectic":[12],"maps":[13,185],"in":[14,82],"1994.":[15],"This":[16],"six-parameter":[17],"generalizes":[19],"H\u00e9non's":[20],"ubiquitous":[21],"2D":[22],"map":[23],"and":[24,81,146],"provides":[25],"local":[27],"approximation":[28],"dynamics":[31,42,106],"more":[33,120],"general":[34],"4D":[35],"maps.":[36],"We":[37],"show":[38],"that":[39,52,94],"bounded":[41,158],"Moser's":[44],"is":[46,85,107],"organized":[47],"by":[48,148],"codimension-three":[50],"bifurcation":[51,57],"creates":[53,75],"four":[54,76],"fixed":[55,77,92,127,140,170],"points---a":[56],"analogous":[58],"to":[59,109,136,178],"doubled,":[61],"saddle-center---which":[62],"we":[63],"call":[64],"quadfurcation.":[66],"In":[67,101],"some":[68],"sectors":[69],"parameter":[71],"space":[72],"quadfurcation":[74,161,176],"points":[78,93,128,141],"from":[79],"none,":[80],"others":[83],"it":[84],"collision":[87],"pair":[90,115,180],"re-emerge":[95],"as":[96],"two":[97,137,167],"or":[98,166],"possibly":[99],"four.":[100],"simplest":[103],"case":[104],"similar":[108],"cross":[111],"product":[112],"H\u00e9non":[117,184],"maps,":[118],"but":[119],"typically":[121],"stability":[123],"created":[126],"does":[129],"not":[130],"have":[131],"this":[132],"simple":[133],"form.":[134],"Up":[135],"can":[142,162],"be":[143],"doubly":[144],"elliptic":[145],"surrounded":[147],"bubbles":[149],"invariant":[151],"two-tori;":[152],"these":[153],"dominate":[154],"set":[156],"orbits.":[159],"The":[160],"also":[163],"create":[164],"one":[165],"complex-unstable":[168],"(Krein)":[169],"points.":[171],"Special":[172],"cases":[173],"correspond":[177],"weakly":[182],"coupled":[183],"near":[186],"their":[187],"saddle-center":[188],"bifurcations.":[189]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2020-02-14T00:00:00"}
