Scaling properties of the measure of constant topological entropy

The topological entropy for some families of one-dimensional unimodal maps is studied. By arranging the windows of constant topological entropy in a binary tree, we have obtained the total measure of these windows. The scaling properties of this measure are studied.     

On a conjecture of Guillemin and Sternberg in geometric quantization of multiplicity-free symplectic spaces

We study the relation between multiplicity-free symplectic manifolds and the multiplicities of group representations obtained by geometric quantization. With the help of a general equivalence theorem we can prove a conjecture of Guillemin and Sternberg in the compact Kähler case.     

Fundamental groups of complements of plane curves and symplectic invariants

Introducing the notion of stabilized fundamental group for the complement of a branch curve in , we define effectively computable invariants of symplectic 4-manifolds that generalize those previously introduced by Moishezon and Teicher for complex projective surfaces. Moreover, we study the structure of these invariants and formulate conjectures supported by calculations on new examples.     

A note on the complementarity problem

We show by an example that, in a complementarity problem where the given map is continuous and monotone on the nonnegative orthant, the existence of a feasible solution is not sufficient to guarantee existence of a solution to the complementarity problem.The author thanks Professor S. Karamardian and Dr. J. More for helpful discussions regarding this note.     

Lower Bound for Energies of Harmonic Tangent Unit-Vector Fields on Convex Polyhedra

We derive a lower bound for energies of harmonic maps of convex polyhedra in to the unit sphere S² with tangent boundary conditions on the faces. We also establish that C maps satisfying tangent boundary conditions are dense with respect to the Sobolev norm in the space of continuous tangent maps of finite energy.This revised version was published online in March 2005 with corrections to the cover date.