Topological conjugacy of locally free 𝐑 n-1 actions on n-manifolds
Annales de l'Institut Fourier, Volume 24 (1974) no. 4, p. 213-227
For actions as in the title we associate a collection of rotation numbers. If one of them is sufficiently irrational then the action is conjugate (as an action) to either a linear action on a torus or to an action on a principal T k bundle over T 2 with T k ×R 1 orbits.
À une action au sens du titre, nous attachons une collection des nombres de rotation. Si l’un des nombres est suffisamment irrationnel, alors l’action est conjuguée (au sens d’une action) soit à une action linéaire sur un tore, soit à une action sur un fibré principal sur T 2 de fibre T k avec les orbites isomorphes à T k ×R 1 .
@article{AIF_1974__24_4_213_0,
     author = {Tischler, David C. and Tischler, Rosamond W.},
     title = {Topological conjugacy of locally free ${\bf R}^{n-1}$ actions on $n$-manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {24},
     number = {4},
     year = {1974},
     pages = {213-227},
     doi = {10.5802/aif.539},
     mrnumber = {52 \#1726},
     zbl = {0287.57016},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_1974__24_4_213_0}
}
Topological conjugacy of locally free ${\bf R}^{n-1}$ actions on $n$-manifolds. Annales de l'Institut Fourier, Volume 24 (1974) no. 4, pp. 213-227. doi : 10.5802/aif.539. https://aif.centre-mersenne.org/item/AIF_1974__24_4_213_0/

[1] R. Sacksteder, Foliations and Pseudogroups, American Journal of Mathematics, 87 (1965), 98-102. | MR 30 #4268 | Zbl 0136.20903

[2] S. Sternberg, Celestial Mechanics, Part II, W. A. Benjamin, New York, 1969. | Zbl 0194.56702

[3] R. Tischler, Thesis, " Conjugacy Problems for Rk Actions ", City University of New York, 1971.

[4] Y. Katznelson, An Introduction to Harmonic Analysis, John Wiley and Sons, New York, 1968. | MR 40 #1734 | Zbl 0169.17902

[5] A. Wintner, The Linear Difference Equation of First Order for Angular Variables, Duke Mathematics Journal, 12 (1945), 445-449. | MR 7,163c | Zbl 0061.20005