{"id":"https://openalex.org/W1994202546","doi":"https://doi.org/10.1090/s0025-5718-00-01242-4","title":"On iterates of M\u00f6bius transformations on fields","display_name":"On iterates of M\u00f6bius transformations on fields","publication_year":2000,"publication_date":"2000-03-06","ids":{"openalex":"https://openalex.org/W1994202546","doi":"https://doi.org/10.1090/s0025-5718-00-01242-4","mag":"1994202546"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01242-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01242-4","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01242-4/S0025-5718-00-01242-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01242-4/S0025-5718-00-01242-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067628981","display_name":"Sam Northshield","orcid":null},"institutions":[{"id":"https://openalex.org/I63475719","display_name":"SUNY Plattsburgh","ror":"https://ror.org/033zmj163","country_code":"US","type":"education","lineage":["https://openalex.org/I63475719"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sam Northshield","raw_affiliation_strings":["Plattsburgh State University, Plattsburgh, New York 12901"],"affiliations":[{"raw_affiliation_string":"Plattsburgh State University, Plattsburgh, New York 12901","institution_ids":["https://openalex.org/I63475719"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067628981"],"corresponding_institution_ids":["https://openalex.org/I63475719"],"apc_list":null,"apc_paid":null,"fwci":0.2832,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58593176,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"235","first_page":"1305","last_page":"1310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9993000030517578,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9993000030517578,"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/T12504","display_name":"Mathematics and Applications","score":0.9961000084877014,"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/T12170","display_name":"History and Theory of Mathematics","score":0.973800003528595,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/mathematics","display_name":"Mathematics","score":0.8193973898887634},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7565251588821411},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42502063512802124},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3332071304321289},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24174907803535461}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8193973898887634},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7565251588821411},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42502063512802124},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3332071304321289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24174907803535461}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-00-01242-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01242-4","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01242-4/S0025-5718-00-01242-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.9774","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.9774","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2001-70-235/S0025-5718-00-01242-4/S0025-5718-00-01242-4.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.3624","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.3624","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.gac.edu/~snorthsh/iter1.ps","raw_type":"text"},{"id":"pmh:oai:dspace.sunyconnect.suny.edu:1951/69944","is_oa":false,"landing_page_url":"http://hdl.handle.net/1951/69944","pdf_url":null,"source":{"id":"https://openalex.org/S4306400078","display_name":"SUNY Digital Repository Support (State University of New York System)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63190737","host_organization_name":"University at Buffalo, State University of New York","host_organization_lineage":["https://openalex.org/I63190737"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:soar.suny.edu:20.500.12648/1123","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.12648/1123","pdf_url":null,"source":{"id":"https://openalex.org/S4306400078","display_name":"SUNY Digital Repository Support (State University of New York System)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63190737","host_organization_name":"University at Buffalo, State University of New York","host_organization_lineage":["https://openalex.org/I63190737"],"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":"Article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01242-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01242-4","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01242-4/S0025-5718-00-01242-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1994202546.pdf","grobid_xml":"https://content.openalex.org/works/W1994202546.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2005463497","https://openalex.org/W2043305097","https://openalex.org/W2329352437","https://openalex.org/W4233634216","https://openalex.org/W4241009969","https://openalex.org/W4247930526","https://openalex.org/W4402918580","https://openalex.org/W4403205968"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,21,36,55,77,136,153,166,180,221,253,287,305],"content-type=\"math/mathml\">":[2,22,37,56,78,137,154,167,181,222,254,288,306],"<mml:math":[3,23,38,57,79,138,155,168,182,223,255,289,307],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,24,39,58,80,139,156,169,183,224,256,290,308],"alttext=\"p\">":[5,59],"<mml:semantics>":[6,27,42,60,94,142,158,171,185,227,258,292,310],"<mml:mi>p</mml:mi>":[7,61],"<mml:annotation":[8,29,44,62,119,144,160,173,187,229,260,294,312],"encoding=\"application/x-tex\">p</mml:annotation>":[9,63],"</mml:semantics>":[10,31,46,64,124,146,162,175,189,231,262,296,314],"</mml:math>":[11,32,47,65,125,147,163,176,190,232,263,297,315],"</inline-formula>":[12,33,48,66,126,148,164,177,191,233,264,298,316],"be":[13,49],"a":[14,18,237,250],"quadratic":[15],"polynomial":[16],"over":[17],"splitting":[19],"field":[20],"alttext=\"upper":[25,40,81,140,225],"K\">":[26,226],"<mml:mi>K</mml:mi>":[28,100,228],"encoding=\"application/x-tex\">K</mml:annotation>":[30,230],",":[34],"and":[35,72,216,243,301,325],"S\">":[41,93,141],"<mml:mi>S</mml:mi>":[43,117,143],"encoding=\"application/x-tex\">S</mml:annotation>":[45,145],"the":[50,151,211,247,275,283,302],"set":[51,135],"of":[52,54,150,198,205,249,270,286,304],"zeros":[53],".":[67,192],"We":[68],"define":[69],"an":[70,195],"associative":[71],"commutative":[73],"binary":[74],"relation":[75],"on":[76],"G":[82],"identical-to":[83],"upper":[84,92],"K":[85],"union":[86],"StartSet":[87],"normal":[88],"infinity":[89],"EndSet":[90],"minus":[91],"<mml:mrow>":[95],"<mml:mi>G</mml:mi>":[96],"<mml:mo>":[97,101,114],"\u2261":[98],"</mml:mo>":[99,103,116],"\u222a":[102],"<mml:mo":[104,111],"fence=\"false\"":[105,112],"stretchy=\"false\">{</mml:mo>":[106],"<mml:mi":[107],"mathvariant=\"normal\">":[108],"\u221e":[109],"</mml:mi>":[110],"stretchy=\"false\">}</mml:mo>":[113],"\u2212":[115],"</mml:mrow>":[118],"encoding=\"application/x-tex\">G\\equiv":[120],"K\\cup":[121],"\\{\\infty":[122],"\\}-S</mml:annotation>":[123],"so":[127],"that":[128,281],"every":[129],"M\u00f6bius":[130,251],"transformation":[131,252],"with":[132,236,322],"fixed":[133,272,284],"point":[134],"is":[149,234],"form":[152],"alttext=\"x\">":[157],"<mml:mi>x</mml:mi>":[159],"encoding=\"application/x-tex\">x</mml:annotation>":[161],"\u201cplus\u201d":[165],"alttext=\"c\">":[170,184],"<mml:mi>c</mml:mi>":[172,186],"encoding=\"application/x-tex\">c</mml:annotation>":[174,188],"for":[178,246],"some":[179],"This":[193],"permits":[194],"easy":[196],"proof":[197],"Aitken":[199],"acceleration":[200],"as":[201,203],"well":[202],"generalizations":[204,328],"known":[206],"results":[207],"concerning":[208],"Newton\u2019s":[209,319],"method,":[210,213,215],"secant":[212],"Halley\u2019s":[214],"higher":[217,326],"order":[218,323,327],"methods.":[219],"If":[220],"equipped":[235],"norm,":[238],"then":[239,318],"we":[240,279],"give":[241],"necessary":[242],"sufficient":[244],"conditions":[245],"iterates":[248,303],"alttext=\"m\">":[257,291,309],"<mml:mi>m</mml:mi>":[259,293,311],"encoding=\"application/x-tex\">m</mml:annotation>":[261,295,313],"to":[265,268],"converge":[266,329],"(necessarily":[267],"one":[269],"its":[271],"points)":[273],"in":[274],"norm":[276],"topology.":[277],"Finally,":[278],"show":[280],"if":[282],"points":[285],"are":[299],"distinct":[300],"converge,":[317],"method":[320],"converges":[321],"2,":[324],"accordingly.":[330]},"counts_by_year":[],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
