10 The Work of Stephen Smale in Differential Topology MORRIS W. HIRSCH Background The theme of this conference is “Unity and Diversity in Mathematics.” The diversity is evident in the many topics covered. Reviewing Smale's work in ...

Obituary of E. H. Spanier

Markets and related games are modeled by several types of deterministic and stochastic dynamical systems. Results are applied to B. Arthur's urn models of stochastic allocation processes, and to repeated games in which players use the long term strategy of fictitious play.

The main result is that the Jacobian determinant of an analytic open map f: ℝn → ℝn does not change sign. A corollary of the proof is that the set of branch points of f has dimension ≤ n - 2. © Birkhäuser Verlag, 2002.

Thinking about the rich social dimensions of ordinary, everyday cash use at the micro level suggests that fungibility is not an automatic function of money, but money’s goal. Fungibility is something that must be achieved. Cash denominations can perhaps be imagined as falling on a fungibility spectrum, ranging from “immediately fungible” on one end, to “fungible through extensive intersubjective mediation” on the other. The many intermediate steps one often needs to take to achieve money’s fungibility in Colca are socially significant, culturally generative, and ethnographically revealing.

Let X ⊂ Rn be a set whose interior is connected and dense in X, ordered by a closed convex cone K ⊂ Rn having nonempty interior. Let T: X ≈ X be an order-preserving homeomorphism. The following result is proved: Assume the set of periodic points of T is dense in X, and K is a polyhedron. Then T is periodic.

If a smooth foliation of a manifold M has a compact leaf L, conditions on the holonomy of L are given ensuriing that every nearby foliation has a unique compact leaf near L.