$3-2-1$ foliations for Reeb flows on the tight 3-sphere
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- by Carolina Lemos de Oliveira
- Trans. Amer. Math. Soc.
- DOI: https://doi.org/10.1090/tran/9119
- Published electronically: April 9, 2024
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Abstract:
We study the existence of $3-2-1$ foliations adapted to Reeb flows on the tight $3$-sphere. These foliations admit precisely three binding orbits whose Conley-Zehnder indices are $3$, $2$, and $1$, respectively. All regular leaves are disks and annuli asymptotic to the binding orbits. Our main results provide sufficient conditions for the existence of $3-2-1$ foliations with prescribed binding orbits. We also exhibit a concrete Hamiltonian on $\mathbb {R}^4$ admitting $3-2-1$ foliations when restricted to suitable energy levels.References
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Bibliographic Information
- Carolina Lemos de Oliveira
- Affiliation: Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rio de Janeiro - RJ, Brasil
- ORCID: 0000-0002-0693-6681
- Email: carolina.lemos@ime.uerj.br
- Received by editor(s): June 12, 2021
- Received by editor(s) in revised form: June 10, 2023, and November 15, 2023
- Published electronically: April 9, 2024
- Additional Notes: This study was financed by grant #2016/10466-5, São Paulo Research Foundation (FAPESP), by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and by Serrapilheira Institute through a grant awarded to Prof. Vinicius Ramos.
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
- MSC (2020): Primary 53D35; Secondary 37J46, 37J55
- DOI: https://doi.org/10.1090/tran/9119