Year: 2010
Type: article
Abstract: Let M be a closed 3-manifold that supports a partially hyperbolic diffeomorphism f . If π 1 ( M ) is nilpotent, the induced action of f * on is partially hyperbolic. If π 1 ( M ) is almost nilpotent or if π 1 ( M ) has subexponential growth, M is finitely covered by a circle bundle over the torus. If π 1 ( M ) is almost solvable, M is finitely covered by a torus bundle over the circle. Furthermore, there exist infinitely many hyperbolic 3-manifolds that do not support dynamically coherent partially hyperbolic diffeomorphisms; this list includes the Weeks manifold. If f is a strong partially hyperbolic diffeomorphism on a closed 3-manifold M and if π 1 ( M ) is nilpotent, then the lifts of the stable and unstable foliations are quasi-isometric in the universal cover of M . It then follows that f is dynamically coherent. We also provide a sufficient condition for dynamical coherence in any dimension. If f is centre-bunched and if the centre-stable and centre-unstable distributions are Lipschitz, then the partially hyperbolic diffeomorphism f must be dynamically coherent.
Source: Nonlinearity
Author: Kamlesh Parwani
Institution: Eastern Illinois University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1965327986