Cyclic pursuit on compact manifolds

Surgery on Compact Manifolds

Lipschitz Spaces on Compact Manifolds

Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...

Expansive Homeomorphisms on Compact Manifolds

In this paper theorems are proved which provide for lifting and projecting expansive homeomorphisms through pseudocovering mappings so that the lift or projection is also an expansive homeomorphism. Using these techniques it is shown that the compact orientable surface of genus 2 admits an expansive homeomorphism.

Continuous Wavelets on Compact Manifolds

Let M be a smooth compact oriented Riemannian manifold, and let ∆M be the Laplace-Beltrami operator on M. Say 0 6= f ∈ S(R), and that f(0) = 0. For t > 0, let Kt(x, y) denote the kernel of f(t∆M). We show that Kt is well-localized near the diagonal, in the sense that it satisfies estimates akin to those satisfied by the kernel of the convolution operator f(t∆) on R. We define continuous S-wavel...

Asynchronous Cyclic Pursuit

In this article we study the convergence of the positions of a multi-agent system in a cyclic pursuit under asynchronism and time delays. Each agent is assumed to operate on an infinite sequence of behaviors modeled by a finite state machine, which is represented by a discrete asynchronous mathematical model on a higher-level. The results on the convergence of the synchronous model is used in t...