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{"title":"具有超越动态度的双元映射","authors":"Jason P. Bell, Jeffrey Diller, Mattias Jonsson, Holly Krieger","doi":"10.1112/plms.12573","DOIUrl":null,"url":null,"abstract":"We give examples of birational selfmaps of <mjx-container aria-label=\"double struck upper P Superscript d Baseline comma d greater than or slanted equals 3\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/plms12573-math-0001.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"2,3,7\" data-semantic-content=\"3\" data-semantic- data-semantic-role=\"sequence\" data-semantic-speech=\"double struck upper P Superscript d Baseline comma d greater than or slanted equals 3\" data-semantic-type=\"punctuated\"><mjx-msup data-semantic-children=\"0,1\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"numbersetletter\" data-semantic-type=\"superscript\"><mjx-mi data-semantic-font=\"double-struck\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"numbersetletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.363em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msup><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"8\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\" rspace=\"3\" style=\"margin-left: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"4,6\" data-semantic-content=\"5\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"inequality\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,⩾\" data-semantic-parent=\"7\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\" rspace=\"5\" space=\"5\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:00246115:media:plms12573:plms12573-math-0001\" display=\"inline\" location=\"graphic/plms12573-math-0001.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"2,3,7\" data-semantic-content=\"3\" data-semantic-role=\"sequence\" data-semantic-speech=\"double struck upper P Superscript d Baseline comma d greater than or slanted equals 3\" data-semantic-type=\"punctuated\"><msup data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-parent=\"8\" data-semantic-role=\"numbersetletter\" data-semantic-type=\"superscript\"><mi data-semantic-=\"\" data-semantic-font=\"double-struck\" data-semantic-parent=\"2\" data-semantic-role=\"numbersetletter\" data-semantic-type=\"identifier\" mathvariant=\"double-struck\">P</mi><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">d</mi></msup><mo data-semantic-=\"\" data-semantic-operator=\"punctuated\" data-semantic-parent=\"8\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\">,</mo><mrow data-semantic-=\"\" data-semantic-children=\"4,6\" data-semantic-content=\"5\" data-semantic-parent=\"8\" data-semantic-role=\"inequality\" data-semantic-type=\"relseq\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">d</mi><mo data-semantic-=\"\" data-semantic-operator=\"relseq,⩾\" data-semantic-parent=\"7\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\">⩾</mo><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\">3</mn></mrow></mrow>$\\mathbb {P}^d, d \\geqslant 3$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, 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.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":"16 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Birational maps with transcendental dynamical degree\",\"authors\":\"Jason P. Bell, Jeffrey Diller, Mattias Jonsson, Holly Krieger\",\"doi\":\"10.1112/plms.12573\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give examples of birational selfmaps of <mjx-container aria-label=\\\"double struck upper P Superscript d Baseline comma d greater than or slanted equals 3\\\" ctxtmenu_counter=\\\"0\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/plms12573-math-0001.png\\\"><mjx-semantics><mjx-mrow data-semantic-children=\\\"2,3,7\\\" data-semantic-content=\\\"3\\\" data-semantic- data-semantic-role=\\\"sequence\\\" data-semantic-speech=\\\"double struck upper P Superscript d Baseline comma d greater than or slanted equals 3\\\" data-semantic-type=\\\"punctuated\\\"><mjx-msup data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"numbersetletter\\\" data-semantic-type=\\\"superscript\\\"><mjx-mi data-semantic-font=\\\"double-struck\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"numbersetletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: 0.363em;\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msup><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"comma\\\" data-semantic-type=\\\"punctuation\\\" rspace=\\\"3\\\" style=\\\"margin-left: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\\\"4,6\\\" data-semantic-content=\\\"5\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,⩾\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\" rspace=\\\"5\\\" space=\\\"5\\\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\\\"true\\\" display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:00246115:media:plms12573:plms12573-math-0001\\\" display=\\\"inline\\\" location=\\\"graphic/plms12573-math-0001.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"2,3,7\\\" data-semantic-content=\\\"3\\\" data-semantic-role=\\\"sequence\\\" data-semantic-speech=\\\"double struck upper P Superscript d Baseline comma d greater than or slanted equals 3\\\" data-semantic-type=\\\"punctuated\\\"><msup data-semantic-=\\\"\\\" data-semantic-children=\\\"0,1\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"numbersetletter\\\" data-semantic-type=\\\"superscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-font=\\\"double-struck\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"numbersetletter\\\" data-semantic-type=\\\"identifier\\\" mathvariant=\\\"double-struck\\\">P</mi><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">d</mi></msup><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"comma\\\" data-semantic-type=\\\"punctuation\\\">,</mo><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"4,6\\\" data-semantic-content=\\\"5\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relseq\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">d</mi><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"relseq,⩾\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\">⩾</mo><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">3</mn></mrow></mrow>$\\\\mathbb {P}^d, d \\\\geqslant 3$</annotation></semantics></math></mjx-assistive-mml></mjx-container>, 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.\",\"PeriodicalId\":49667,\"journal\":{\"name\":\"Proceedings of the London Mathematical Society\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2023-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1112/plms.12573\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1112/plms.12573","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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