{"id":"https://openalex.org/W4385335509","doi":"https://doi.org/10.1137/22m1504986","title":"Hausdorff Dimension of Cantor Intersections and Robust Heterodimensional Cycles for Heterochaos Horseshoe Maps","display_name":"Hausdorff Dimension of Cantor Intersections and Robust Heterodimensional Cycles for Heterochaos Horseshoe Maps","publication_year":2023,"publication_date":"2023-07-28","ids":{"openalex":"https://openalex.org/W4385335509","doi":"https://doi.org/10.1137/22m1504986"},"language":"en","primary_location":{"id":"doi:10.1137/22m1504986","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1504986","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/A5016464152","display_name":"Yoshitaka Saiki","orcid":"https://orcid.org/0000-0002-3184-0577"},"institutions":[{"id":"https://openalex.org/I111428342","display_name":"Hitotsubashi University","ror":"https://ror.org/04jqj7p05","country_code":"JP","type":"education","lineage":["https://openalex.org/I111428342"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yoshitaka Saiki","raw_affiliation_strings":["Graduate School of Business Administration, Hitotsubashi University, Tokyo, 186-8601, Japan"],"raw_orcid":"https://orcid.org/0000-0002-3184-0577","affiliations":[{"raw_affiliation_string":"Graduate School of Business Administration, Hitotsubashi University, Tokyo, 186-8601, Japan","institution_ids":["https://openalex.org/I111428342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074038990","display_name":"Hiroki Takahasi","orcid":"https://orcid.org/0000-0002-0295-126X"},"institutions":[{"id":"https://openalex.org/I203951103","display_name":"Keio University","ror":"https://ror.org/02kn6nx58","country_code":"JP","type":"education","lineage":["https://openalex.org/I203951103"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroki Takahasi","raw_affiliation_strings":["Keio Institute of Pure and Applied Sciences (KiPAS), Department of Mathematics, Keio University, Yokohama, 223-8522, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Keio Institute of Pure and Applied Sciences (KiPAS), Department of Mathematics, Keio University, Yokohama, 223-8522, Japan","institution_ids":["https://openalex.org/I203951103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022360238","display_name":"James A. Yorke","orcid":"https://orcid.org/0000-0002-9599-0136"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James A. Yorke","raw_affiliation_strings":["Institute for Physical Science and Technology and Mathematics and Physics Departments, University of Maryland, College Park, MD 20742, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Physical Science and Technology and Mathematics and Physics Departments, University of Maryland, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016464152"],"corresponding_institution_ids":["https://openalex.org/I111428342"],"apc_list":null,"apc_paid":null,"fwci":1.5832,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.79706452,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"22","issue":"3","first_page":"1852","last_page":"1876"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9998000264167786,"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":0.9998000264167786,"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":0.967199981212616,"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":0.9492999911308289,"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/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.8544313907623291},{"id":"https://openalex.org/keywords/cantor-set","display_name":"Cantor set","score":0.8367866277694702},{"id":"https://openalex.org/keywords/cantor-function","display_name":"Cantor function","score":0.7247259020805359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7103469967842102},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6824026107788086},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.627135157585144},{"id":"https://openalex.org/keywords/effective-dimension","display_name":"Effective dimension","score":0.5933343172073364},{"id":"https://openalex.org/keywords/elementary-proof","display_name":"Elementary proof","score":0.4886022210121155},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4456515908241272},{"id":"https://openalex.org/keywords/packing-dimension","display_name":"Packing dimension","score":0.418844997882843},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.3842334449291229},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.3070424199104309},{"id":"https://openalex.org/keywords/minkowski\u2013bouligand-dimension","display_name":"Minkowski\u2013Bouligand dimension","score":0.27386218309402466},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2560904026031494}],"concepts":[{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.8544313907623291},{"id":"https://openalex.org/C36605576","wikidata":"https://www.wikidata.org/wiki/Q273188","display_name":"Cantor set","level":2,"score":0.8367866277694702},{"id":"https://openalex.org/C149701218","wikidata":"https://www.wikidata.org/wiki/Q938883","display_name":"Cantor function","level":3,"score":0.7247259020805359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7103469967842102},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6824026107788086},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.627135157585144},{"id":"https://openalex.org/C115311070","wikidata":"https://www.wikidata.org/wiki/Q5347255","display_name":"Effective dimension","level":3,"score":0.5933343172073364},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.4886022210121155},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4456515908241272},{"id":"https://openalex.org/C80661125","wikidata":"https://www.wikidata.org/wiki/Q5404299","display_name":"Packing dimension","level":5,"score":0.418844997882843},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.3842334449291229},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.3070424199104309},{"id":"https://openalex.org/C101597101","wikidata":"https://www.wikidata.org/wiki/Q2555655","display_name":"Minkowski\u2013Bouligand dimension","level":4,"score":0.27386218309402466},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2560904026031494},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1504986","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1504986","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5099999904632568}],"awards":[{"id":"https://openalex.org/G1283065318","display_name":null,"funder_award_id":"19K21835","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2009351370","display_name":null,"funder_award_id":"19KK0067","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3359878305","display_name":null,"funder_award_id":"20H01811","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W47527881","https://openalex.org/W141353907","https://openalex.org/W1975482467","https://openalex.org/W1976931460","https://openalex.org/W2018554867","https://openalex.org/W2043301921","https://openalex.org/W2059625173","https://openalex.org/W2067789687","https://openalex.org/W2068136282","https://openalex.org/W2076794290","https://openalex.org/W2084164774","https://openalex.org/W2093699033","https://openalex.org/W2107807777","https://openalex.org/W2133143355","https://openalex.org/W2152054319","https://openalex.org/W2331123169","https://openalex.org/W2493052075","https://openalex.org/W2589483636","https://openalex.org/W2963117407","https://openalex.org/W2990821190","https://openalex.org/W3119256308","https://openalex.org/W3164699369","https://openalex.org/W3179549713","https://openalex.org/W4238652859","https://openalex.org/W4239981491","https://openalex.org/W4250260852","https://openalex.org/W4255802976"],"related_works":["https://openalex.org/W228299209","https://openalex.org/W2031336817","https://openalex.org/W310539813","https://openalex.org/W2366593328","https://openalex.org/W2146603951","https://openalex.org/W165284569","https://openalex.org/W2089667061","https://openalex.org/W3191035861","https://openalex.org/W2084337755","https://openalex.org/W2358654324"],"abstract_inverted_index":{".As":[0],"a":[1,5,17,73,82],"model":[2],"to":[3],"provide":[4],"hands-on,":[6],"elementary":[7],"understanding":[8],"of":[9,21,23,32,40,47,51,66,76,95,103],"chaotic":[10],"dynamics":[11],"in":[12],"dimension":[13,53,78],"3,":[14],"we":[15,84],"introduce":[16],"\\(C^2\\)":[18,86],"-open":[19],"set":[20,39,46,75],"diffeomorphisms":[22],"\\(\\mathbb":[24],"R^3\\)":[25],"having":[26],"two":[27],"horseshoes":[28],"with":[29],"different":[30],"dimensions":[31],"instability.":[33],"We":[34],"prove":[35],"that":[36,63],"the":[37,44,48,64,67,93,101],"unstable":[38,68],"one":[41],"horseshoe":[42],"and":[43,62,69,100],"stable":[45,70],"other":[49],"are":[50,59],"Hausdorff":[52,77],"nearly":[54,79],"2":[55],"whose":[56],"cross":[57],"sections":[58],"Cantor":[60,104],"sets":[61,71],"intersection":[65],"contains":[72],"fractal":[74],"1.":[80],"As":[81],"corollary":[83],"detect":[85],"-robust":[87],"heterodimensional":[88],"cycles.":[89],"Our":[90],"proof":[91],"employs":[92],"theory":[94],"normally":[96],"hyperbolic":[97],"invariant":[98],"manifolds":[99],"thicknesses":[102],"sets.Keywordshorseshoe":[105],"mapCantor":[106],"setsthicknessHausdorff":[107],"dimensionheterodimensional":[108],"cyclesMSC":[109],"codes37C2937C4537G25":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}