{"id":"https://openalex.org/W2067222304","doi":"https://doi.org/10.1137/090776329","title":"Computation of Heteroclinic Arcs with Application to the Volume Preserving H\u00e9non Family","display_name":"Computation of Heteroclinic Arcs with Application to the Volume Preserving H\u00e9non Family","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2067222304","doi":"https://doi.org/10.1137/090776329","mag":"2067222304"},"language":"en","primary_location":{"id":"doi:10.1137/090776329","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090776329","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":["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/A5088549920","display_name":"J. D. Mireles James","orcid":"https://orcid.org/0000-0001-8449-9408"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. D. Mireles James","raw_affiliation_strings":["University of Texas at Austin#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Austin#TAB#","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049444402","display_name":"H\u00e9ctor E. Lomel\u0131\u0301","orcid":null},"institutions":[{"id":"https://openalex.org/I187481652","display_name":"Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico","ror":"https://ror.org/029md1766","country_code":"MX","type":"education","lineage":["https://openalex.org/I187481652"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Hector Lomel\u00ed","raw_affiliation_strings":["Instituto Tecnol\u00f3gico Auton\u00f3mo de M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto Tecnol\u00f3gico Auton\u00f3mo de M\u00e9xico","institution_ids":["https://openalex.org/I187481652"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8326,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.90606231,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"9","issue":"3","first_page":"919","last_page":"953"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9965000152587891,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9951000213623047,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.991599977016449,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diffeomorphism","display_name":"Diffeomorphism","score":0.617911696434021},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5421687960624695},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5197727084159851},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5172503590583801},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5029217600822449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4787982404232025},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4552653133869171},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.45074066519737244},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2842041552066803},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.2828875184059143},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1083926260471344}],"concepts":[{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.617911696434021},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5421687960624695},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5197727084159851},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5172503590583801},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5029217600822449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4787982404232025},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4552653133869171},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.45074066519737244},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2842041552066803},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2828875184059143},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1083926260471344},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090776329","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090776329","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:CiteSeerX.psu:10.1.1.330.151","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.330.151","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ma.utexas.edu/mp_arc/c/10/10-3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.333.1275","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.333.1275","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.utexas.edu/users/jjames/preprints/JamesLomeliPaperSIAM.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W19005950","https://openalex.org/W48894704","https://openalex.org/W74169033","https://openalex.org/W143062967","https://openalex.org/W175617483","https://openalex.org/W1583979427","https://openalex.org/W1660935327","https://openalex.org/W1963890921","https://openalex.org/W1964822948","https://openalex.org/W1968892491","https://openalex.org/W1973584024","https://openalex.org/W1983135841","https://openalex.org/W1989018928","https://openalex.org/W1997980245","https://openalex.org/W1998778871","https://openalex.org/W2000018344","https://openalex.org/W2003884541","https://openalex.org/W2003888782","https://openalex.org/W2020348013","https://openalex.org/W2026029035","https://openalex.org/W2036319645","https://openalex.org/W2041957871","https://openalex.org/W2046238971","https://openalex.org/W2055610195","https://openalex.org/W2059903013","https://openalex.org/W2067865347","https://openalex.org/W2073686912","https://openalex.org/W2077011938","https://openalex.org/W2080089157","https://openalex.org/W2083922917","https://openalex.org/W2089655837","https://openalex.org/W2090963365","https://openalex.org/W2116731876","https://openalex.org/W2119779417","https://openalex.org/W2150878689","https://openalex.org/W2158223566","https://openalex.org/W2752853835","https://openalex.org/W3033171690","https://openalex.org/W3099526877","https://openalex.org/W3102317020","https://openalex.org/W3123094903","https://openalex.org/W3192909774"],"related_works":["https://openalex.org/W4386794506","https://openalex.org/W2962984814","https://openalex.org/W4293508317","https://openalex.org/W3104281043","https://openalex.org/W2075372083","https://openalex.org/W2462155254","https://openalex.org/W2891397405","https://openalex.org/W4212817163","https://openalex.org/W3217798761","https://openalex.org/W4384920019"],"abstract_inverted_index":{"Let":[0],"$f:\\mathbb{R}^3\\rightarrow\\mathbb{R}^3$":[1],"be":[2],"a":[3,23,31,53,95,115],"diffeomorphism":[4],"with":[5,86],"$p_0,p_1\\in\\mathbb{R}^3$":[6],"distinct":[7],"hyperbolic":[8],"fixed":[9],"points.":[10],"Assume":[11],"that":[12,82],"$W^u(p_0)$":[13],"and":[14,38,51,77,84,100,135],"$W^s(p_1)$":[15],"are":[16,42],"two-dimensional":[17],"manifolds":[18],"which":[19],"intersect":[20],"transversally":[21],"at":[22],"point":[24],"q.":[25],"Then":[26,89],"the":[27,58,90,110,121,130],"intersection":[28,91],"is":[29],"locally":[30],"one-dimensional":[32],"smooth":[33],"arc":[34,92,122],"$\\tilde{\\gamma}$":[35,41,61,93],"through":[36],"q,":[37],"points":[39],"on":[40],"orbits":[43],"heteroclinic":[44],"from":[45],"$p_0$":[46],"to":[47,62],"$p_1$.":[48],"We":[49,65,102,124],"describe":[50],"implement":[52],"numerical":[54,106,126],"scheme":[55,107],"for":[56,108,129],"computing":[57,68],"jets":[59],"of":[60,73,120],"arbitrary":[63],"order.":[64],"begin":[66],"by":[67],"high":[69,116],"order":[70,117],"polynomial":[71],"approximations":[72],"some":[74,137],"functions":[75],"$P_u,P_s:\\mathbb{R}^2\\rightarrow\\mathbb{R}^3$,":[76],"domain":[78],"disks":[79],"$D_u,D_s\\subset\\mathbb{R}^2$,":[80],"such":[81],"$W_{loc}^u(p_0)=P_u(D_u)$":[83],"$W_{loc}^s(p_1)=P_s(D_s)$":[85],"$W_{loc}^u(p_0)\\cap":[87],"W_{loc}^s(p_1)\\neq\\emptyset$.":[88],"solves":[94],"functional":[96,111],"equation":[97],"involving":[98],"$P_s$":[99],"$P_u$.":[101],"develop":[103],"an":[104],"iterative":[105],"solving":[109],"equation,":[112],"resulting":[113],"in":[114],"Taylor":[118],"expansion":[119],"$\\tilde{\\gamma}$.":[123],"present":[125],"example":[127],"computations":[128],"volume":[131],"preserving":[132],"H\u00e9non":[133],"family":[134],"compute":[136],"global":[138],"invariant":[139],"branched":[140],"manifolds.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}