{"id":"https://openalex.org/W2551723219","doi":null,"title":"The Art of Iterating Rational Functions over Finite Fields","display_name":"The Art of Iterating Rational Functions over Finite Fields","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2551723219","mag":"2551723219"},"language":"en","primary_location":{"id":"mag:2551723219","doi":null,"is_oa":false,"landing_page_url":"https://www.birs.ca/workshops/2013/13w5141/report13w5141.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5069834567","display_name":"Nigel Boston","orcid":"https://orcid.org/0000-0002-2807-4963","observed_orcids":["https://orcid.org/0000-0002-2807-4963"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nigel Boston","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2807-4963","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061265713","display_name":"Michael E. Zieve","orcid":"https://orcid.org/0000-0002-3872-3736","observed_orcids":["https://orcid.org/0000-0002-3872-3736"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael E. Zieve","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3872-3736","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.5067999958992004,"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":0.5067999958992004,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.45210000872612,"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.00570000009611249,"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/arithmetic-dynamics","display_name":"arithmetic dynamics","score":0.6639999747276306},{"id":"https://openalex.org/keywords/periodic-points","display_name":"periodic points","score":0.703000009059906},{"id":"https://openalex.org/keywords/cycle-length","display_name":"cycle length","score":0.8849999904632568},{"id":"https://openalex.org/keywords/cryptography","display_name":"cryptography","score":0.34599998593330383},{"id":"https://openalex.org/keywords/non-archimedean-dynamics","display_name":"non-Archimedean dynamics","score":0.625},{"id":"https://openalex.org/keywords/p-adic-dynamics","display_name":"p-adic dynamics","score":0.5090000033378601}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6385075449943542},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5935207009315491},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.5827136635780334},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5678069591522217},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5495055913925171},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5490666627883911},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.48401138186454773},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4655054211616516},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4625057578086853},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44877681136131287},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.4386165738105774},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3056018054485321},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24626490473747253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20261678099632263},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.10141581296920776},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2551723219","doi":null,"is_oa":false,"landing_page_url":"https://www.birs.ca/workshops/2013/13w5141/report13w5141.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W7123824","https://openalex.org/W8767028","https://openalex.org/W1499658123","https://openalex.org/W1973457877","https://openalex.org/W1979024814","https://openalex.org/W2030211942","https://openalex.org/W2054591280","https://openalex.org/W2061510313","https://openalex.org/W2066838126","https://openalex.org/W2069039276","https://openalex.org/W2071124910","https://openalex.org/W2072754428","https://openalex.org/W2104731923","https://openalex.org/W2150898678","https://openalex.org/W2226303357","https://openalex.org/W2949477212","https://openalex.org/W2963519414"],"related_works":["https://openalex.org/W7097265837","https://openalex.org/W1593383640","https://openalex.org/W2481821895","https://openalex.org/W2013368481","https://openalex.org/W2140628278","https://openalex.org/W1915577777","https://openalex.org/W7100855444","https://openalex.org/W3037652233","https://openalex.org/W4402586993","https://openalex.org/W315047097"],"abstract_inverted_index":{"The":[0,79,182,288],"field":[1,76],"of":[2,9,18,28,44,49,77,87,117,123,128,161,173,184,203,270,298,316,322,332,352,375,385,390,409],"complex":[3,251,343],"dynamical":[4,38,148,216,263,324,344],"systems":[5,39,217,325],"generated":[6],"by":[7,199,417],"iteration":[8,43],"polynomials":[10],"and":[11,24,101,106,119,146,155,164,185,206,224,258,291,302,311,329,349,366,399],"rational":[12,45,156],"functions":[13,46],"is":[14,336],"a":[15,21,25,75,112,139],"classical":[16],"area":[17,315],"mathematics":[19],"with":[20,111],"rich":[22],"history":[23],"wide":[26,378],"variety":[27],"results.":[29],"Recently,":[30],"there":[31],"has":[32,190,278],"been":[33,58,97,104,109,192,279,414],"substantial":[34],"interest":[35,186],"in":[36,67,89,92,187,208,232,244,273,295,339,363],"arithmetical":[37],"(ADS),":[40],"meaning":[41],"the":[42,61,68,124,132,179,195,200,234,320,330,350,373,383,388,403,407,421],"over":[47,194,284,326],"fields":[48,328],"number-theoretic":[50],"interest.":[51],"Although":[52],"isolated":[53],"results":[54],"regarding":[55,372],"ADS":[56,71,129],"have":[57,83,96,103,108,212,356,412],"proven":[59],"throughout":[60],"twentieth":[62],"century,":[63],"it":[64],"was":[65,240,248],"only":[66],"1990\u2019s":[69],"that":[70,239],"were":[72],"identified":[73],"as":[74,218,220,406],"study.":[78],"past":[80],"two":[81],"decades":[82],"seen":[84],"an":[85,299],"explosion":[86],"work":[88],"this":[90,188,209,228,267,410],"topic,":[91],"which":[93,137,174,211,247,335],"fundamental":[94],"problems":[95,294,362,404],"solved,":[98],"new":[99,140],"questions":[100,371,381],"conjectures":[102],"posed,":[105],"connections":[107],"forged":[110],"great":[113],"many":[114],"different":[115],"areas":[116],"pure":[118],"applied":[120],"mathematics.":[121],"Indications":[122],"fast":[125],"growing":[126],"significance":[127,183],"also":[130,191],"include":[131,152],"2010":[133],"Mathematics":[134],"Subject":[135],"Classification,":[136],"contains":[138],"section,":[141],"37Pxx,":[142],"devoted":[143],"to":[144,178,262,358,361],"arithmetic":[145,256],"non-archimedean":[147],"systems,":[149],"whose":[150,306],"subsections":[151],"37P05":[153],"(Polynomial":[154],"maps),":[157],"37P35":[158],"(Arithmetic":[159,166],"properties":[160],"periodic":[162],"points),":[163],"37P55":[165],"dynamics":[167],"on":[168,236,250,281,319,382],"general":[169],"algebraic":[170,301],"varieties),":[171],"all":[172],"are":[175,297],"directly":[176],"related":[177,274],"proposed":[180,405],"workshop.":[181],"topic":[189],"evidenced":[193],"last":[196],"several":[197],"years":[198],"large":[201],"number":[202,225,303,384],"international":[204],"meetings":[205],"workshops":[207],"area,":[210],"attracted":[213],"experts":[214,221],"from":[215,222,342],"well":[219],"algebra":[223],"theory.":[226],"From":[227],"list":[229],"we":[230],"note":[231],"particular":[233],"program":[235],"Dynamical":[237,282],"Systems":[238,283],"held":[241],"at":[242],"ICERM":[243],"Spring":[245],"2012,":[246],"focused":[249],"dynamics,":[252,254,257],"p-adic":[253],"global":[255],"moduli":[259],"spaces":[260],"associated":[261],"systems.":[264,345,368],"However,":[265],"despite":[266],"recent":[268],"profusion":[269],"scientific":[271],"activity":[272],"areas,":[275],"little":[276],"progress":[277],"made":[280],"Finite":[285],"Fields":[286],"(DFF).":[287],"present":[289,338],"exciting":[290],"challenging":[292],"mathematical":[293,310],"DFF":[296,376],"intricate":[300],"theoretic":[304],"flavour":[305],"study":[307,331],"requires":[308],"deep":[309],"computational":[312],"tools.":[313],"This":[314],"research":[317],"focuses":[318],"construction":[321],"non-classical":[323],"finite":[327],"atypical":[333],"behaviour":[334,355],"not":[337],"standard":[340],"constructions":[341,348],"Such":[346],"novel":[347],"classification":[351],"their":[353],"anomalous":[354],"led":[357],"innovative":[359],"solutions":[360],"cryptography,":[364],"biological":[365],"physical":[367],"Many":[369],"important":[370],"orbits":[374],"remain":[377],"open,":[379],"including":[380],"aperiodic":[386],"points,":[387],"size":[389],"orbit":[391],"intersections":[392],"(in":[393],"linearly":[394],"disjoint":[395],"DFF),":[396],"cycle":[397],"lengths,":[398],"so":[400],"on.":[401],"Furthermore,":[402],"goal":[408],"proposal":[411],"barely":[413],"touched":[415],"upon":[416],"other":[418,422],"meetings.":[419],"On":[420],"hand,":[423]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-11-30T00:00:00"}
