Circle homeomorphisms and shears

We give parameterizations of homeomorphisms, quasisymmetric maps and symmetric maps of the unit circle in terms of shear coordinates for the Farey tesselation.Comment: 26 pages, 3 figure

Periods, Lefschetz numbers and entropy for a class of maps on a bouquet of circles

We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions of our maps on both the fundamental group and the first homology group.Comment: 19 pages, 2 figure

Computation of Bhat's OMIT maps with different coefficients

The OMIT electron-density-map calculation is very effective in discovering errors in a macromolecular structure determination. A Fortran program called OMIT has been written to calculate such maps and an investigation has been carried out into which coefficients for the map calculation produce the best OMIT maps. Testing of the program on Savinase showed that the best overall results were obtained when |Fo| without figure of merit was used. In regions where the map is incorrect, the most interesting OMIT maps are produced when only the figure of merit, or modified SIGMAA coefficients, are used as the initial map amplitude coefficients. Thus, these tests suggest that such OMIT maps are particularly useful to reconstruct the macromolecular model in the grossly incorrect regions of the model.

The Space of Harmonic Maps from the 2-sphere to the Complex Projective Plane

We study the topology of the space of harmonic maps from $S^2$ to \CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for the space of harmonic maps to$\CP n$for$n\geq 2$. We show that the components of maps to$\CP 2$ are complex manifolds.Comment: Plain TeX, 11 pages, no figure

Anticipating the dynamics of chaotic maps

We study the regime of anticipated synchronization in unidirectionally coupled chaotic maps such that the slave map has its own output reinjected after a certain delay. For a class of simple maps, we give analytic conditions for the stability of the synchronized solution, and present results of numerical simulations of coupled 1D Bernoulli-like maps and 2D Baker maps, that agree well with the analytic predictions.Comment: Uses the elsart.cls (v2000) style (included). 9 pages, including 4 figures. New version contains minor modifications to text and figure

Value sets of bivariate Chebyshev maps over finite fields

We determine the cardinality of the value sets of bivariate Chebyshev maps over finite fields. We achieve this using the dynamical properties of these maps and the algebraic expressions of their fixed points in terms of roots of unity.Comment: 11 pages, 2 figure

On the two-point function of general planar maps and hypermaps

We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points at a prescribed distance. The maps considered here may have faces of arbitrarily large degree, which requires new bijections to be tackled. We obtain exact expressions for the following cases: general and bipartite maps counted by their number of edges, 3-hypermaps and 3-constellations counted by their number of dark faces, and finally general and bipartite maps counted by both their number of edges and their number of faces.Comment: 32 pages, 17 figure