We discover a rigidity phenomenon within the volume-preserving partially hyperbolic
diffeomorphisms with 1-dimensional center. In particular, for smooth ergodic perturbations of …

In this paper we study the centralizer of flows and R^ d R d-actions on compact Riemannian
manifolds. We prove that the centralizer of every C^ ∞ C∞ Komuro-expansive flow with non …

In this paper we study the problem of knowing when the centralizer of a vector field is
“small”. We obtain several criteria that imply different types of “small” centralizers, namely …

We show that Thurston's earthquake flow is strongly asymmetric in the sense that its
normalizer is as small as possible inside the group of orbifold automorphisms of the bundle …

In the late nineties, Smale proposed a list of problems for the next century, and, among
these, it was conjectured that for every $ r\ge 1$ a $ C^ r $-generic diffeomorphism has trivial …

This paper is devoted to the study of the space of discrete symmetries of smooth flows and
their time-t maps, namely the space of diffeomorphisms which commute with a flow and its …

We show that generic C∞ hyperbolic flows commute with noC∞-diffeomorphism other than
a time-t map of the flow itself. Kinematic-expansivity, a substantial weakening of expansivity …

In this paper we study the diffeomorphism centralizer of a vector field: given a vector field it is
the set of diffeomorphisms that commutes with the flow. Our main theorem states that for a …

Anosov diffeomorphisms on $\mathbb T^ d $ are well known to be topologically conjugate to
hyperbolic automorphisms induced by integer valued matrices. We show that in general the …

Given r⩾ 1, the discrete C r-centralizer of a vector field is formed by the set of its symmetries,
that is, the set of C r-diffeomorphisms commuting with the flow generated by it. Here we …