Orbit Structure of certain ${\mathbb{R}}^{2}$-actions on solid torus

C. Maquera; L. F. Martins

doi:10.5802/afst.1195

Orbit Structure of certain

ℝ^{2}

-actions on solid torus

C. Maquera ¹; L. F. Martins ²

¹ Departamento de Matemática, USP – Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Caixa Postal 668, CEP 13560-970, São Carlos, SP, Brazil. Work supported by FAPESP of Brazil Grant 02/09425-0.
² Departamento de Matemática, UNESP – Universidade Estadual Paulista, Instituto de Biologia, Letras e Ciências Exatas, R. Cristóvão Colombo, 2265, Jardim Nazareth, 15054-000, São José do Rio Preto, SP, Brazil. Work supported by FAPESP of Brazil Grant 98/13400-5

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 3, pp. 613-633.

Abstract
Abstract

In this paper we describe the orbit structure of $C^{2}$ -actions of $ℝ^{2}$ on the solid torus $S^{1} \times D^{2}$ having $S^{1} \times {0}$ and $S^{1} \times \partial D^{2}$ as the only compact orbits, and $S^{1} \times {0}$ as singular set.

Nous décrivons la structure des orbites des actions de class $C^{2}$ de $ℝ^{2}$ sur le tore solide $S^{1} \times D^{2}$ ayant uniquement $S^{1} \times {0}$ et $S^{1} \times \partial D^{2}$ comme orbites compacts, et $S^{1} \times {0}$ comme ensemble singulier.

MR Zbl

DOI: 10.5802/afst.1195

Author's affiliations:

C. Maquera ¹; L. F. Martins ²

¹ Departamento de Matemática, USP – Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Caixa Postal 668, CEP 13560-970, São Carlos, SP, Brazil. Work supported by FAPESP of Brazil Grant 02/09425-0.
² Departamento de Matemática, UNESP – Universidade Estadual Paulista, Instituto de Biologia, Letras e Ciências Exatas, R. Cristóvão Colombo, 2265, Jardim Nazareth, 15054-000, São José do Rio Preto, SP, Brazil. Work supported by FAPESP of Brazil Grant 98/13400-5

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     author = {C. Maquera and L. F. Martins},
     title = {Orbit {Structure} of certain ${\mathbb{R}}^{2}$-actions on solid torus},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {613--633},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
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     volume = {Ser. 6, 17},
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C. Maquera; L. F. Martins. Orbit Structure of certain ${\mathbb{R}}^{2}$-actions on solid torus. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 3, pp. 613-633. doi : 10.5802/afst.1195. https://afst.centre-mersenne.org/articles/10.5802/afst.1195/

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