This paper addresses the coordinated control problem of underactuated thrustpropelled vehicles in the presence of irregular communication delays under a directed communication graph topology. We propose a distributed control algorithm that drives the vehicles to a prescribed formation provided that the communication graph contains a spanning tree. Using the multi-dimensional small-gain approach...

In connection with his interest in selfdistributive algebra, Richard Laver established two deep results with potential applications in low-dimensional topology, namely the existence of what is now known as the Laver tables and the well-foundedness of the standard ordering of positive braids. Here we present these results and discuss the way they could be used in topological applications. Richar...

The Jacobi identity is the key relation in the definition of a Lie algebra. In the last decade, it also appeared at the heart of the theory of finite type invariants of knots, links and 3-manifolds (and is there called the IHX-relation). In addition, this relation was recently found to arise naturally in a theory of embedding obstructions for 2-spheres in 4-manifolds [20]. We expose the underly...

We show how to measure the failure of the Whitney move in dimension 4 by constructing higher-order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants such as Milnor, Sato-Levine, and Arf invariants. We al...

Many a dissipative evolution equation possesses a global attractor A with finite Hausdorff dimension d. In this paper it is shown there is an embedding X of A into IR , with N = [2d+2], such that X is the global attractor of some finite-dimensional system on IR with trivial dynamics on X. This allows the construction of a discrete dynamical system on IR which reproduces the dynamics of the time...