This note contains some remarks about the homologies that can be associated to a foliation which is invariant and uniformly expanded by a diffeomorphism. We construct a family of 'dynamical' closed currents supported on the foliation which help us relate the geometric volume growth of the leaves under the diffeomorphism with the map induced on homology in the case when these currents have nonzero homology.
|Number of pages||12|
|Journal||Discrete and Continuous Dynamical Systems - Series S|
|State||Published - 1 Jun 2009|
- Expanding dynamics
- Invariant foliations
- Ruelle-Sullivan currents