3-2-1 foliations for Reeb flows on the tight 3-sphere

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-01-17 DOI:10.1090/tran/9119

Carolina de Oliveira

{"title":"3-2-1 foliations for Reeb flows on the tight 3-sphere","authors":"Carolina de Oliveira","doi":"10.1090/tran/9119","DOIUrl":null,"url":null,"abstract":"<p>We study the existence of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3 minus 2 minus 1\"> <mml:semantics> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">3-2-1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> foliations adapted to Reeb flows on the tight <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=\"application/x-tex\">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-sphere. These foliations admit precisely three binding orbits whose Conley-Zehnder indices are <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=\"application/x-tex\">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding=\"application/x-tex\">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1\"> <mml:semantics> <mml:mn>1</mml:mn> <mml:annotation encoding=\"application/x-tex\">1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, respectively. All regular leaves are disks and annuli asymptotic to the binding orbits. Our main results provide sufficient conditions for the existence of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3 minus 2 minus 1\"> <mml:semantics> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">3-2-1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> foliations with prescribed binding orbits. We also exhibit a concrete Hamiltonian on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R Superscript 4\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mn>4</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">\\mathbb {R}^4</mml:annotation> </mml:semantics> </mml:math> </inline-formula> admitting <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3 minus 2 minus 1\"> <mml:semantics> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">3-2-1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> foliations when restricted to suitable energy levels.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/tran/9119","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

We study the existence of 3 − 2 − 1 3-2-1 foliations adapted to Reeb flows on the tight 3 3 -sphere. These foliations admit precisely three binding orbits whose Conley-Zehnder indices are 3 3 , 2 2 , and 1 1 , respectively. All regular leaves are disks and annuli asymptotic to the binding orbits. Our main results provide sufficient conditions for the existence of 3 − 2 − 1 3-2-1 foliations with prescribed binding orbits. We also exhibit a concrete Hamiltonian on R 4 \mathbb {R}^4 admitting 3 − 2 − 1 3-2-1 foliations when restricted to suitable energy levels.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

紧密三球面上里布流的 3-2-1 叶形

我们研究了紧 3 3 -球面上适应里布流的 3 - 2 - 1 3-2-1 叶形的存在。这些叶形恰好包含三个结合轨道，它们的康利-泽恩德指数分别为 3 3、2 2 和 1 1。所有规则叶片都是渐近于结合轨道的圆盘和环面。我们的主要结果为具有规定结合轨道的 3 - 2 - 1 3-2-1 叶形的存在提供了充分条件。我们还展示了 R 4 \mathbb {R}^4 上的一个具体哈密顿，当限制在合适的能级时，它允许 3 - 2 - 1 3-2-1 对折。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

期刊最新文献

Management of Cholesteatoma: Hearing Rehabilitation. Congenital Cholesteatoma. Evaluation of Cholesteatoma. Management of Cholesteatoma: Extension Beyond Middle Ear/Mastoid. Recidivism and Recurrence.