Browsing Citations Only by Author "Basener, William"
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The Brouwer Fixed Point Theorem applied to rumour transmission
Basener, William; Ross, David; Brooks, Bernard (Elsevier Science B.V., Amsterdam, 2006-08)The results of the Brouwer Fixed Point Theorem are extended to continuous dynamical systems. It is shown that if there exists a compact convex positive invariant set for the dynamical system, then this convex positive ... -
Every nonsingular C1 flow on a closed manifold of dimension greater than two has a global transverse disk
Basener, William (Elsevier Science B.V., Amsterdam, 2004-01-01)We prove three results about global cross sections which are disks, henceforth called global transverse disks. First we prove that every nonsingular (fixed point free) C^1 flow on a closed (compact, no boundary) connected ... -
Global cross sections and minimal flows
Basener, William (Elsevier Science B.V., Amsterdam, 2002-06-30)Let M be a closed n-dimensional manifold with a flow () that has a global cross section Sigma ~= D^(n-1), and let h be the (piecewise continuous) first return map for Sigma. Our primary examples of such flows are minimal ... -
Knots and topologically transitive flows on 3-manifolds
Basener, William (Elsevier Science B.V., Amsterdam, 2004-05)Suppose that () is a nonsingular (fixed point free) flow on a smooth three-dimensional manifold M. Suppose the orbit though a point p ∈M is dense in M. Let D be an imbedded disk in M containing p which is transverse to ... -
Periodic prime knots and topologically transitive flows on 3-manifolds
Basener, William; Sullivan, Michael (Elsevier Science B.V., Amsterdam, 2006-02-01)Suppose that () is a nonsingular (fixed point free) C^1 flow on a smooth closed 3-dimensional manifold M with H2(M) = 0. Suppose that () has a dense orbit. We show that there exists an open dense set N µ M such that any ...