The topology of group extensions of C systems
Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 453-465
Voir la notice de l'article provenant de la source Math-Net.Ru
The paper is concerned with the topological and metric properties of group extensions of C systems. The basic theorem describes the topologically transitive component, the ergodic component, and the K component of a group extension of a C system. It is shown that each of these components is a group sub-bundle of a principal bundle in which the group extension acts. The frame flow on a manifold of negative curvature is seen to be a special case of a group of extension of a C system. It is shown that the space of frames on a compact three-dimensional manifold with negative curvature does not have any group sub-bundles, so that the frame flow on manifolds of this class is topologically transitive, ergodic, and a K system.
@article{MZM_1975_18_3_a14,
author = {M. I. Brin},
title = {The topology of group extensions of {C} systems},
journal = {Matemati\v{c}eskie zametki},
pages = {453--465},
publisher = {mathdoc},
volume = {18},
number = {3},
year = {1975},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a14/}
}
M. I. Brin. The topology of group extensions of C systems. Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 453-465. http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a14/