On simultaneous linearization of diffeomorphisms of the sphere
Dolgopyat, Dmitry ; Krikorian, Raphaël
Duke Math. J., Tome 136 (2007) no. 1, p. 475-505 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Let $R_1, R_2,\ldots,R_m$ be rotations generating ${\mathbb{SO}}_{d+1}$ , $d\geq 2$ , and let $f_1, f_2,\ldots,f_m$ be small smooth perturbations of them. We show that $\{f_\alpha\}$ can be linearized simultaneously if and only if the associated random walk has zero Lyapunov exponents. As a consequence, we obtain stable ergodicity of actions of random rotations in even dimensions
Publié le : 2007-02-15
Classification:  37C85,  37H15,  70H08 
@article{1170084896,
     author = {Dolgopyat, Dmitry and Krikorian, Rapha\"el},
     title = {On simultaneous linearization of diffeomorphisms of the sphere},
     journal = {Duke Math. J.},
     volume = {136},
     number = {1},
     year = {2007},
     pages = { 475-505},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1170084896}
}

Dolgopyat, Dmitry; Krikorian, Raphaël. On simultaneous linearization of diffeomorphisms of the sphere. Duke Math. J., Tome 136 (2007) no. 1, pp.  475-505. http://gdmltest.u-ga.fr/item/1170084896/