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

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-01-17 DOI:10.1090/tran/9119

Carolina de Oliveira

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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.

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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。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.