{"id":"https://openalex.org/W2117887226","doi":"https://doi.org/10.1142/s0218127411028301","title":"PARAMETERIZED DYNAMICS FOR THE WEIERSTRASS ELLIPTIC FUNCTION OVER SQUARE PERIOD LATTICES","display_name":"PARAMETERIZED DYNAMICS FOR THE WEIERSTRASS ELLIPTIC FUNCTION OVER SQUARE PERIOD LATTICES","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2117887226","doi":"https://doi.org/10.1142/s0218127411028301","mag":"2117887226"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127411028301","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411028301","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5110104789","display_name":"Jane Hawkins","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JANE HAWKINS","raw_affiliation_strings":["Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Chapel Hill, NC 27599-3250, USA","Department of Mathematics , University of North Carolina at Chapel Hill , CB #3250, Chapel Hill, NC 27599-3250 , USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Chapel Hill, NC 27599-3250, USA","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"Department of Mathematics , University of North Carolina at Chapel Hill , CB #3250, Chapel Hill, NC 27599-3250 , USA","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049025210","display_name":"Mark McClure","orcid":"https://orcid.org/0000-0001-5381-740X"},"institutions":[{"id":"https://openalex.org/I87097829","display_name":"University of North Carolina at Asheville","ror":"https://ror.org/017c6at71","country_code":"US","type":"education","lineage":["https://openalex.org/I87097829"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"MARK MCCLURE","raw_affiliation_strings":["Department of Mathematics,of North Carolina at Asheville, Asheville, North Carolina, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics,of North Carolina at Asheville, Asheville, North Carolina, USA","institution_ids":["https://openalex.org/I87097829"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110104789"],"corresponding_institution_ids":["https://openalex.org/I114027177"],"apc_list":null,"apc_paid":null,"fwci":0.4298,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.5985677,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"01","first_page":"125","last_page":"135"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":1.0,"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":1.0,"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/T12162","display_name":"Cellular Automata and Applications","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.989300012588501,"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/mandelbrot-set","display_name":"Mandelbrot set","score":0.8437864184379578},{"id":"https://openalex.org/keywords/julia-set","display_name":"Julia set","score":0.8342151641845703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7256273627281189},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.6261504888534546},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6009915471076965},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5560120940208435},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5377514362335205},{"id":"https://openalex.org/keywords/holomorphic-function","display_name":"Holomorphic function","score":0.5189785361289978},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47540220618247986},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46715229749679565},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.45375868678092957},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41946542263031006},{"id":"https://openalex.org/keywords/complex-dynamics","display_name":"Complex dynamics","score":0.4161861538887024},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2165279984474182},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2027539610862732},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09417277574539185}],"concepts":[{"id":"https://openalex.org/C97519476","wikidata":"https://www.wikidata.org/wiki/Q257","display_name":"Mandelbrot set","level":3,"score":0.8437864184379578},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.8342151641845703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7256273627281189},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.6261504888534546},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6009915471076965},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5560120940208435},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5377514362335205},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.5189785361289978},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47540220618247986},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46715229749679565},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.45375868678092957},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41946542263031006},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.4161861538887024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2165279984474182},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2027539610862732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09417277574539185},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127411028301","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411028301","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W50293812","https://openalex.org/W141117032","https://openalex.org/W1533967041","https://openalex.org/W1628277156","https://openalex.org/W1700084322","https://openalex.org/W2008507922","https://openalex.org/W2009203625","https://openalex.org/W2065629179","https://openalex.org/W2077482988","https://openalex.org/W2082735186","https://openalex.org/W2088131781","https://openalex.org/W2113893822","https://openalex.org/W2114177365","https://openalex.org/W2165853527","https://openalex.org/W2798095799","https://openalex.org/W3102739121","https://openalex.org/W4205524157","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2372579255","https://openalex.org/W1972311046","https://openalex.org/W2169256438","https://openalex.org/W4308870400","https://openalex.org/W4391023542","https://openalex.org/W2165507669","https://openalex.org/W4240246673","https://openalex.org/W1597671403","https://openalex.org/W3043713331","https://openalex.org/W2054520167"],"abstract_inverted_index":{"We":[0,22,89],"iterate":[1],"the":[2,11,14,17,29,33,67,79,86,93,97,110],"Weierstrass":[3],"elliptic":[4],"\u2118":[5,83],"function":[6],"in":[7,50,113],"order":[8,106],"to":[9,47],"understand":[10],"dependence":[12,31],"of":[13,69,82,104],"dynamics":[15,95,111],"on":[16,24,32,101,109],"underlying":[18],"period":[19],"lattice":[20],"L.":[21],"focus":[23],"square":[25],"lattices":[26],"and":[27,63,78,96],"use":[28],"holomorphic":[30],"classical":[34],"invariants":[35],"(g":[36,43,53],"2":[37,44,54],",":[38,45],"g":[39],"3":[40],")":[41],"=":[42],"0)":[46],"show":[48,90],"that":[49,91],"parameter":[51,114],"space":[52,115],"-space)":[55],"one":[56],"sees":[57],"both":[58,92],"quadratic-like":[59],"attracting":[60],"orbit":[61],"behavior":[62],"prepole":[64,70,98,102],"dynamics.":[65],"In":[66],"case":[68],"parameters":[71,99,103],"all":[72],"critical":[73],"orbits":[74],"terminate":[75],"at":[76],"poles":[77],"Julia":[80],"set":[81],"L":[84],"is":[85],"entire":[87],"sphere.":[88],"Mandelbrot-like":[94],"accumulate":[100],"lower":[105],"providing":[107],"results":[108],"occurring":[112],"\"between":[116],"Mandelbrot":[117],"sets\".":[118]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
