Bicritical Rational Maps With a Common Iterate

Abstract Let $f$ be a degree $d$ bicritical rational map with critical point set $\mathcal{C}_f$ and critical value set $\mathcal{V}_f$. Using the group $\textrm{Deck}(f^k)$ of deck transformations of $f^k$, we show that if $g$ is a bicritical rational map that shares an iterate with $f$, then $\mat...

Full description

Saved in:
Bibliographic Details
Published in:International mathematics research notices 2024-01, Vol.2024 (2), p.1568-1605
Main Authors: Koch, Sarah, Lindsey, Kathryn, Sharland, Thomas
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c224t-8293177577bf313de10791dab31ed36d4ebb776ecf0eacbd29647eb10013b493
container_end_page 1605
container_issue 2
container_start_page 1568
container_title International mathematics research notices
container_volume 2024
creator Koch, Sarah
Lindsey, Kathryn
Sharland, Thomas
description Abstract Let $f$ be a degree $d$ bicritical rational map with critical point set $\mathcal{C}_f$ and critical value set $\mathcal{V}_f$. Using the group $\textrm{Deck}(f^k)$ of deck transformations of $f^k$, we show that if $g$ is a bicritical rational map that shares an iterate with $f$, then $\mathcal{C}_f = \mathcal{C}_g$ and $\mathcal{V}_f = \mathcal{V}_g$. Using this, we show that if two bicritical rational maps of even degree $d$ share an iterate, then they share a second iterate, and both maps belong to the symmetry locus of degree $d$ bicritical rational maps.
doi_str_mv 10.1093/imrn/rnad041
format article
fullrecord <record><control><sourceid>oup_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1093_imrn_rnad041</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><oup_id>10.1093/imrn/rnad041</oup_id><sourcerecordid>10.1093/imrn/rnad041</sourcerecordid><originalsourceid>FETCH-LOGICAL-c224t-8293177577bf313de10791dab31ed36d4ebb776ecf0eacbd29647eb10013b493</originalsourceid><addsrcrecordid>eNp9j0tLAzEUhYMoWKs7f8Ds3DjtvUmcO1lqsVqoCFJwOeQ1GOk8SOLCf--Udu3qnMXHOXyM3SIsEJRYhi72y9hrBxLP2Ayrmkrgks6nDiRKUry-ZFcpfQNwwFrM2OIp2BhysHpffOgchn4qb3pMxWfIX4UuVkPXDX2xyT7q7K_ZRav3yd-ccs526-fd6rXcvr9sVo_b0nIuc1lzJZDogci0AoXz071Cp41A70TlpDeGqPK2Ba-tcVxVkrxBABRGKjFn98dZG4eUom-bMYZOx98GoTmoNgfV5qQ64XdHfPgZ_yf_ADjIVUU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Bicritical Rational Maps With a Common Iterate</title><source>Oxford University Press:Jisc Collections:OUP Read and Publish 2024-2025 (2024 collection) (Reading list)</source><creator>Koch, Sarah ; Lindsey, Kathryn ; Sharland, Thomas</creator><creatorcontrib>Koch, Sarah ; Lindsey, Kathryn ; Sharland, Thomas</creatorcontrib><description>Abstract Let $f$ be a degree $d$ bicritical rational map with critical point set $\mathcal{C}_f$ and critical value set $\mathcal{V}_f$. Using the group $\textrm{Deck}(f^k)$ of deck transformations of $f^k$, we show that if $g$ is a bicritical rational map that shares an iterate with $f$, then $\mathcal{C}_f = \mathcal{C}_g$ and $\mathcal{V}_f = \mathcal{V}_g$. Using this, we show that if two bicritical rational maps of even degree $d$ share an iterate, then they share a second iterate, and both maps belong to the symmetry locus of degree $d$ bicritical rational maps.</description><identifier>ISSN: 1073-7928</identifier><identifier>EISSN: 1687-0247</identifier><identifier>DOI: 10.1093/imrn/rnad041</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>International mathematics research notices, 2024-01, Vol.2024 (2), p.1568-1605</ispartof><rights>The Author(s) 2023. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com. 2023</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c224t-8293177577bf313de10791dab31ed36d4ebb776ecf0eacbd29647eb10013b493</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Koch, Sarah</creatorcontrib><creatorcontrib>Lindsey, Kathryn</creatorcontrib><creatorcontrib>Sharland, Thomas</creatorcontrib><title>Bicritical Rational Maps With a Common Iterate</title><title>International mathematics research notices</title><description>Abstract Let $f$ be a degree $d$ bicritical rational map with critical point set $\mathcal{C}_f$ and critical value set $\mathcal{V}_f$. Using the group $\textrm{Deck}(f^k)$ of deck transformations of $f^k$, we show that if $g$ is a bicritical rational map that shares an iterate with $f$, then $\mathcal{C}_f = \mathcal{C}_g$ and $\mathcal{V}_f = \mathcal{V}_g$. Using this, we show that if two bicritical rational maps of even degree $d$ share an iterate, then they share a second iterate, and both maps belong to the symmetry locus of degree $d$ bicritical rational maps.</description><issn>1073-7928</issn><issn>1687-0247</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9j0tLAzEUhYMoWKs7f8Ds3DjtvUmcO1lqsVqoCFJwOeQ1GOk8SOLCf--Udu3qnMXHOXyM3SIsEJRYhi72y9hrBxLP2Ayrmkrgks6nDiRKUry-ZFcpfQNwwFrM2OIp2BhysHpffOgchn4qb3pMxWfIX4UuVkPXDX2xyT7q7K_ZRav3yd-ccs526-fd6rXcvr9sVo_b0nIuc1lzJZDogci0AoXz071Cp41A70TlpDeGqPK2Ba-tcVxVkrxBABRGKjFn98dZG4eUom-bMYZOx98GoTmoNgfV5qQ64XdHfPgZ_yf_ADjIVUU</recordid><startdate>20240122</startdate><enddate>20240122</enddate><creator>Koch, Sarah</creator><creator>Lindsey, Kathryn</creator><creator>Sharland, Thomas</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240122</creationdate><title>Bicritical Rational Maps With a Common Iterate</title><author>Koch, Sarah ; Lindsey, Kathryn ; Sharland, Thomas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c224t-8293177577bf313de10791dab31ed36d4ebb776ecf0eacbd29647eb10013b493</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Koch, Sarah</creatorcontrib><creatorcontrib>Lindsey, Kathryn</creatorcontrib><creatorcontrib>Sharland, Thomas</creatorcontrib><collection>CrossRef</collection><jtitle>International mathematics research notices</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Koch, Sarah</au><au>Lindsey, Kathryn</au><au>Sharland, Thomas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bicritical Rational Maps With a Common Iterate</atitle><jtitle>International mathematics research notices</jtitle><date>2024-01-22</date><risdate>2024</risdate><volume>2024</volume><issue>2</issue><spage>1568</spage><epage>1605</epage><pages>1568-1605</pages><issn>1073-7928</issn><eissn>1687-0247</eissn><abstract>Abstract Let $f$ be a degree $d$ bicritical rational map with critical point set $\mathcal{C}_f$ and critical value set $\mathcal{V}_f$. Using the group $\textrm{Deck}(f^k)$ of deck transformations of $f^k$, we show that if $g$ is a bicritical rational map that shares an iterate with $f$, then $\mathcal{C}_f = \mathcal{C}_g$ and $\mathcal{V}_f = \mathcal{V}_g$. Using this, we show that if two bicritical rational maps of even degree $d$ share an iterate, then they share a second iterate, and both maps belong to the symmetry locus of degree $d$ bicritical rational maps.</abstract><pub>Oxford University Press</pub><doi>10.1093/imrn/rnad041</doi><tpages>38</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1073-7928
ispartof International mathematics research notices, 2024-01, Vol.2024 (2), p.1568-1605
issn 1073-7928
1687-0247
language eng
recordid cdi_crossref_primary_10_1093_imrn_rnad041
source Oxford University Press:Jisc Collections:OUP Read and Publish 2024-2025 (2024 collection) (Reading list)
title Bicritical Rational Maps With a Common Iterate
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-03T07%3A42%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-oup_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Bicritical%20Rational%20Maps%20With%20a%20Common%20Iterate&rft.jtitle=International%20mathematics%20research%20notices&rft.au=Koch,%20Sarah&rft.date=2024-01-22&rft.volume=2024&rft.issue=2&rft.spage=1568&rft.epage=1605&rft.pages=1568-1605&rft.issn=1073-7928&rft.eissn=1687-0247&rft_id=info:doi/10.1093/imrn/rnad041&rft_dat=%3Coup_cross%3E10.1093/imrn/rnad041%3C/oup_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c224t-8293177577bf313de10791dab31ed36d4ebb776ecf0eacbd29647eb10013b493%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_oup_id=10.1093/imrn/rnad041&rfr_iscdi=true