A vector eld on a connected Lie group is said to be linear if its ow is a one parameter group of automorphisms. A control-a ne system is linear if the drift is linear and the controlled vector elds right invariant. The controllability properties of such systems are studied, mainly in the case where the derivation of the group Lie algebra that can be associated to the linear vector eld is inner....

since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modi ed version o...

The object studied in this paper is a pair ((; Y), where is a random surface in I R N and Y random vector eld on I R N. The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector eld Y is smooth outside but may have discontinuities on. Gauss' divergence theorem is applied to derive a ow conservation law for Y. For I R 1 this specializes to a well-known rat...

We present a method to compute enclosures of the local invariant manifolds of a hyperbolic saddle of an analytic vector eld. By considering parametrisations of the invariant manifolds, instead of describing them as graphs of functions from the corresponding tangent spaces, we nd simple recursive formulae for their Taylor coe cients. In addition to this, we obtain rigorous bounds on the remainde...

We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize the construction to tensor fields. A Lie derivative along any (also non left invariant) vector field is proposed and a puzzling ambiguity in its definition di...

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

For a class of hhgher dimensional autonomous systems that have an invariant aane manifold, conditions are derived to preclude the existence of periodic solutions on the invariant manifold. It is established that these conditions are robust under certain type of local perturbations of the vector eld. As a consequence, each bounded semitrajectory on the invariant manifold is shown to converge to ...

We study the equation Xu = f where X belongs to a class of area-preserving vector elds, having saddle-type singularities, on a compact orientable surface M of genus g 2. For a \full measure" set of such vector elds we prove the existence, for any suuciently smooth complex valued function f in a nite codimensional subspace, of a nitely diierentiable solution u. The loss of derivativesis nite, bu...