{"id":"https://openalex.org/W2099264981","doi":"https://doi.org/10.1137/040612877","title":"Symbolic Codes for Rotational Orbits","display_name":"Symbolic Codes for Rotational Orbits","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2099264981","doi":"https://doi.org/10.1137/040612877","mag":"2099264981"},"language":"en","primary_location":{"id":"doi:10.1137/040612877","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612877","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/nlin/0408015","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"H. R. Dullin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"H. R. Dullin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"J. D. Meiss","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. D. Meiss","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"D. G. Sterling","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. G. Sterling","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.18435258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"4","issue":"3","first_page":"515","last_page":"562"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.6836000084877014,"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":0.6836000084877014,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.03200000151991844,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.028999999165534973,"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/continuation","display_name":"Continuation","score":0.6965000033378601},{"id":"https://openalex.org/keywords/symbolic-dynamics","display_name":"Symbolic dynamics","score":0.6843000054359436},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5602999925613403},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4772999882698059},{"id":"https://openalex.org/keywords/rotation-number","display_name":"Rotation number","score":0.45350000262260437},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.44760000705718994},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.43389999866485596},{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"Rotational symmetry","score":0.42080000042915344}],"concepts":[{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6965000033378601},{"id":"https://openalex.org/C16101541","wikidata":"https://www.wikidata.org/wiki/Q1350838","display_name":"Symbolic dynamics","level":2,"score":0.6843000054359436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6420999765396118},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5602999925613403},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4772999882698059},{"id":"https://openalex.org/C135007989","wikidata":"https://www.wikidata.org/wiki/Q643156","display_name":"Rotation number","level":3,"score":0.45350000262260437},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.44760000705718994},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.43389999866485596},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.42080000042915344},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.41830000281333923},{"id":"https://openalex.org/C2776095079","wikidata":"https://www.wikidata.org/wiki/Q489538","display_name":"The Symbolic","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.3621000051498413},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.35659998655319214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34940001368522644},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33640000224113464},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C2775978667","wikidata":"https://www.wikidata.org/wiki/Q7069654","display_name":"Numerical continuation","level":4,"score":0.30320000648498535},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C151602998","wikidata":"https://www.wikidata.org/wiki/Q485287","display_name":"Analytic continuation","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.25699999928474426}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040612877","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612877","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:nlin/0408015","is_oa":true,"landing_page_url":"http://arxiv.org/abs/nlin/0408015","pdf_url":"https://arxiv.org/pdf/nlin/0408015","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:nlin/0408015","is_oa":true,"landing_page_url":"http://arxiv.org/abs/nlin/0408015","pdf_url":"https://arxiv.org/pdf/nlin/0408015","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W92074458","https://openalex.org/W1581792503","https://openalex.org/W1970553514","https://openalex.org/W1972494225","https://openalex.org/W1974926772","https://openalex.org/W1978912613","https://openalex.org/W1979245447","https://openalex.org/W1982349476","https://openalex.org/W1982750906","https://openalex.org/W1991100653","https://openalex.org/W2001105261","https://openalex.org/W2008775492","https://openalex.org/W2015306990","https://openalex.org/W2016173714","https://openalex.org/W2017502732","https://openalex.org/W2017581703","https://openalex.org/W2023400173","https://openalex.org/W2032296316","https://openalex.org/W2036420340","https://openalex.org/W2041442504","https://openalex.org/W2041674289","https://openalex.org/W2043420689","https://openalex.org/W2043992273","https://openalex.org/W2050559829","https://openalex.org/W2050592460","https://openalex.org/W2051185337","https://openalex.org/W2053708782","https://openalex.org/W2058477532","https://openalex.org/W2064210050","https://openalex.org/W2067277512","https://openalex.org/W2068654798","https://openalex.org/W2068710044","https://openalex.org/W2073692875","https://openalex.org/W2078590371","https://openalex.org/W2079659692","https://openalex.org/W2083237407","https://openalex.org/W2090957015","https://openalex.org/W2091668920","https://openalex.org/W2125566231","https://openalex.org/W2139504330","https://openalex.org/W4206252072","https://openalex.org/W4206805073","https://openalex.org/W4302049606"],"related_works":[],"abstract_inverted_index":{"Symbolic":[0],"codes":[1,16],"for":[2,9,40],"rotational":[3,46],"orbits":[4],"and":[5,44],"\"islands-around-islands\"":[6],"are":[7,17,49],"constructed":[8,68],"the":[10,28,41,62,72,76],"quadratic,":[11],"area-preserving":[12],"H\u00e9non":[13],"map.":[14,77],"The":[15,57],"based":[18],"upon":[19],"continuation":[20],"from":[21,27,69],"an":[22],"anti-integrable":[23],"limit":[24],"or,":[25],"alternatively,":[26],"horseshoe.":[29],"Given":[30],"any":[31],"sequence":[32],"of":[33,61,66,71,75],"rotation":[34],"numbers":[35],"we":[36],"obtain":[37],"symbolic":[38,59],"sequences":[39],"corresponding":[42],"elliptic":[43],"hyperbolic":[45],"orbits.":[47],"These":[48],"shown":[50],"to":[51],"be":[52],"consistent":[53],"with":[54],"numerical":[55],"evidence.":[56],"resulting":[58],"partition":[60],"phase":[63],"space":[64],"consists":[65],"wedges":[67],"images":[70],"symmetry":[73],"lines":[74]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2016-06-24T00:00:00"}
