Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds

Classification of Partially Hyperbolic Diffeomorphisms in 3-manifolds with Solvable Fundamental Group

A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, it is dynamically coherent and leaf conjugate to a known algebraic example. This classification includes manifolds which support Anosov flows, and it confirms...

Partially Hyperbolic Diffeomorphisms with a Trapping Property

We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.

Hyperbolic 2-Dimensional Manifolds with 3-Dimensional Automorphism Group

If M is a connected n-dimensional Kobayashi-hyperbolic complex manifold, then the group Aut(M) of holomorphic automorphisms of M is a (real) Lie group in the compact-open topology, of dimension d(M) not exceeding n + 2n, with the maximal value occurring only for manifolds holomorphically equivalent to the unit ball B ⊂ C [Ko1], [Ka]. We are interested in describing hyperbolic manifolds with low...

Hyperbolic 2-Dimensional Manifolds with 3-Dimensional Automorphism Groups I

Let M be a Kobayashi-hyperbolic 2-dimensional complex manifold and Aut(M) the group of holomorphic automorphisms of M . We showed earlier that if dimAut(M) = 3, then Aut(M)-orbits are closed submanifolds in M of (real) codimension 1 or 2. In this paper we classify all connected Kobayashi-hyperbolic 2-dimensional manifolds with 3-dimensional automorphism groups in the case when every orbit has c...