Vol. 1 (1995) #1

JDCS vol. 1 #1 (1995), pp. 1-138

1. F.H. Clarke, Yu. Ledyaev, R.J. Stern, P.R. Wolenski
QUALITATIVE PROPERTIES OF TRAJECTORIES OF CONTROL SYSTEMS: A SURVEY, pp. 1 - 48: We present a unified approach to a complex of related issues in control theory, one based to a great extent on the methods of nonsmooth analysis. The issues include invariance, stability, equilibria, monotonicity, the Hamilton- Jacobi equation, feedback synthesis, and necessary conditions.
2. R. Montgomery
A SURVEY OF SINGULAR CURVES IN SUB-RIEMANNIAN GEOMETRY, pp. 49 - 90: Sub-Riemannian geometry is the geometry of a distribution of k-planes on an n-dimensional manifold with a smoothly varying inner product on the k-planes. Singular curves are singularities of the space of paths tangent to the distribution and joining two fixed points. This survey is devoted to the singular curves, which can be length minimizing geodesics, independent of the choice of inner product.
3. A.G. Khovanskii
TOPOLOGICAL OBSTRUCTIONS TO THE REPRESENTABILITY OF FUNCTIONS BY QUADRATURES, pp. 91 - 123: A topological variant of the Galois theory, in which the monodromy group plays the role of the Galois group, is described. It turns out that there are topological restrictions on the way the Riemann surface of a function represented by quadratures covers the complex plane.
4. D.V. Anosov
FLOWS ON CLOSED SURFACES AND BEHAVIOR OF TRAJECTORIES LIFTED TO THE UNIVERSAL COVERING PLANE, pp. 125 - 138: A survey of works concerning a kind of generalization of the Poincare rotation number for a rather general class of flows on closed surfaces is given. The idea (going back to A.Weil) is to replace this number by the asymptotic direction at infinity of the trajectory lifted to the universal covering plane. Other works on flows on surfaces are also mentioned, but this is done primarily for comparison in order to shed light on the subject.