Birational maps with transcendental dynamical degree

We give examples of birational selfmaps of Pd,d⩾3$\mathbb {P}^d, d \geqslant 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation.

Saved in:
Bibliographic Details
Published in:Proceedings of the London Mathematical Society 2024-01, Vol.128 (1), p.n/a, Article Paper No. e12573, 47
Main Authors: Bell, Jason P., Diller, Jeffrey, Jonsson, Mattias, Krieger, Holly
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c3093-8a523c6dfe82b594105c1705f2bb7a0799c22cede544390482ed58f6dd06bfdc3
cites cdi_FETCH-LOGICAL-c3093-8a523c6dfe82b594105c1705f2bb7a0799c22cede544390482ed58f6dd06bfdc3
container_end_page n/a
container_issue 1
container_start_page
container_title Proceedings of the London Mathematical Society
container_volume 128
creator Bell, Jason P.
Diller, Jeffrey
Jonsson, Mattias
Krieger, Holly
description We give examples of birational selfmaps of Pd,d⩾3$\mathbb {P}^d, d \geqslant 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation.
doi_str_mv 10.1112/plms.12573
format article
fullrecord <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1112_plms_12573</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>PLMS12573</sourcerecordid><originalsourceid>FETCH-LOGICAL-c3093-8a523c6dfe82b594105c1705f2bb7a0799c22cede544390482ed58f6dd06bfdc3</originalsourceid><addsrcrecordid>eNp9j0tLxDAUhYMoWEc3_oKuhY43z7ZLHXxBRUEFdyHNQyNtpySFof_edupKxNU9cM934EPoHMMaY0wu-6aNa0x4Tg9QgpmAjDD2fogSAMIygTE_RicxfgGAoJQniF37oAa_7VSTtqqP6c4Pn-kQVBe17Yzthulhxk61Xs_JfgRrT9GRU020Zz93hd5ub14391n1dPewuaoyTaGkWaE4oVoYZwtS85Jh4BrnwB2p61xBXpaaEG2N5YzRElhBrOGFE8aAqJ3RdIUull0dtjEG62QffKvCKDHI2VfOvnLvO5XhV1n7Ya822fjmbwQvyM43dvxnXD5Xjy8L8w2yoWlJ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Birational maps with transcendental dynamical degree</title><source>Wiley</source><creator>Bell, Jason P. ; Diller, Jeffrey ; Jonsson, Mattias ; Krieger, Holly</creator><creatorcontrib>Bell, Jason P. ; Diller, Jeffrey ; Jonsson, Mattias ; Krieger, Holly</creatorcontrib><description>We give examples of birational selfmaps of Pd,d⩾3$\mathbb {P}^d, d \geqslant 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation.</description><identifier>ISSN: 0024-6115</identifier><identifier>EISSN: 1460-244X</identifier><identifier>DOI: 10.1112/plms.12573</identifier><language>eng</language><ispartof>Proceedings of the London Mathematical Society, 2024-01, Vol.128 (1), p.n/a, Article Paper No. e12573, 47</ispartof><rights>2023 The Authors. is copyright © London Mathematical Society.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3093-8a523c6dfe82b594105c1705f2bb7a0799c22cede544390482ed58f6dd06bfdc3</citedby><cites>FETCH-LOGICAL-c3093-8a523c6dfe82b594105c1705f2bb7a0799c22cede544390482ed58f6dd06bfdc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Bell, Jason P.</creatorcontrib><creatorcontrib>Diller, Jeffrey</creatorcontrib><creatorcontrib>Jonsson, Mattias</creatorcontrib><creatorcontrib>Krieger, Holly</creatorcontrib><title>Birational maps with transcendental dynamical degree</title><title>Proceedings of the London Mathematical Society</title><description>We give examples of birational selfmaps of Pd,d⩾3$\mathbb {P}^d, d \geqslant 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation.</description><issn>0024-6115</issn><issn>1460-244X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>24P</sourceid><recordid>eNp9j0tLxDAUhYMoWEc3_oKuhY43z7ZLHXxBRUEFdyHNQyNtpySFof_edupKxNU9cM934EPoHMMaY0wu-6aNa0x4Tg9QgpmAjDD2fogSAMIygTE_RicxfgGAoJQniF37oAa_7VSTtqqP6c4Pn-kQVBe17Yzthulhxk61Xs_JfgRrT9GRU020Zz93hd5ub14391n1dPewuaoyTaGkWaE4oVoYZwtS85Jh4BrnwB2p61xBXpaaEG2N5YzRElhBrOGFE8aAqJ3RdIUull0dtjEG62QffKvCKDHI2VfOvnLvO5XhV1n7Ya822fjmbwQvyM43dvxnXD5Xjy8L8w2yoWlJ</recordid><startdate>202401</startdate><enddate>202401</enddate><creator>Bell, Jason P.</creator><creator>Diller, Jeffrey</creator><creator>Jonsson, Mattias</creator><creator>Krieger, Holly</creator><scope>24P</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>202401</creationdate><title>Birational maps with transcendental dynamical degree</title><author>Bell, Jason P. ; Diller, Jeffrey ; Jonsson, Mattias ; Krieger, Holly</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3093-8a523c6dfe82b594105c1705f2bb7a0799c22cede544390482ed58f6dd06bfdc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bell, Jason P.</creatorcontrib><creatorcontrib>Diller, Jeffrey</creatorcontrib><creatorcontrib>Jonsson, Mattias</creatorcontrib><creatorcontrib>Krieger, Holly</creatorcontrib><collection>Wiley Open Access</collection><collection>CrossRef</collection><jtitle>Proceedings of the London Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bell, Jason P.</au><au>Diller, Jeffrey</au><au>Jonsson, Mattias</au><au>Krieger, Holly</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Birational maps with transcendental dynamical degree</atitle><jtitle>Proceedings of the London Mathematical Society</jtitle><date>2024-01</date><risdate>2024</risdate><volume>128</volume><issue>1</issue><epage>n/a</epage><artnum>Paper No. e12573, 47</artnum><issn>0024-6115</issn><eissn>1460-244X</eissn><abstract>We give examples of birational selfmaps of Pd,d⩾3$\mathbb {P}^d, d \geqslant 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation.</abstract><doi>10.1112/plms.12573</doi><tpages>47</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0024-6115
ispartof Proceedings of the London Mathematical Society, 2024-01, Vol.128 (1), p.n/a, Article Paper No. e12573, 47
issn 0024-6115
1460-244X
language eng
recordid cdi_crossref_primary_10_1112_plms_12573
source Wiley
title Birational maps with transcendental dynamical degree
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-06T15%3A03%3A19IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Birational%20maps%20with%20transcendental%20dynamical%20degree&rft.jtitle=Proceedings%20of%20the%20London%20Mathematical%20Society&rft.au=Bell,%20Jason%20P.&rft.date=2024-01&rft.volume=128&rft.issue=1&rft.epage=n/a&rft.artnum=Paper%20No.%20e12573,%2047&rft.issn=0024-6115&rft.eissn=1460-244X&rft_id=info:doi/10.1112/plms.12573&rft_dat=%3Cwiley_cross%3EPLMS12573%3C/wiley_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c3093-8a523c6dfe82b594105c1705f2bb7a0799c22cede544390482ed58f6dd06bfdc3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true