123207928
The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift
Mixtures of polyisocyanates are prepared in one step by reacting phosgene with a slurry of selected polyamines in an inert solvent.
121662994
Uniformization of attracting basins for exponential maps
Soit la famille exponentielle complexe Eλ(Z)=λ exp(Z). Il y a un ensemble ouvert de valeurs de λ dans le plan complexe pour lesquelles Eλ a un point fixe attractif unique; Ωλ est le bassin d'attraction pour ces valeurs. On considere l'uniformisation Φλ de Ωλ et on etudie la dynamique induite par Φλ sur le disque unite
53559839
Fixed points of polynomial maps. Part II. Fixed point portraits
— Douady, Hubbard and Branner have introduced the concept of a "limb" in the Mandelbrot set. A quadratic map f(z) = z + c belongs to the p/q-limb if and only if there exist q external rays of its Julia set which land at a common fixed point of/, and which are permuted by/with combinatorial rotation number ^^Q/Z, p / q ^ O . (Compare Figure 1 and Appendix C, as well as Lemma 2.2.) This note will make a similar analysis of higher degree polynomials by introducing the concept of the "fixed point portrait" of a monic polynomial map.
123137491
A finiteness theorem for a dynamical class of entire functions
123686855
On the shape of the unit sphere in Q(Δ)
We show that the unit sphere in the Banach space of L 1 holomorphic quadratic differentials on the disk is weakly uniformly convex with exponent 1/2 at certain points
126013684
Fixed points of polynomial maps. I. Rotation subsets of the circles
— We give a combinatorial analysis of rational rotation subsets of the circle. These are invariant subsets that have well-defined rational rotation numbers under the standard self-covering maps of S. This analysis has applications to the classification of dynamical systems generated by polynomials in one complex variable.
533051
Volatility of the short rate in the rational lognormal model
Abstract. A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among practioners and academics alike. However, it turns out to have the undesirable feature of predicting that the asymptotic value of the short rate volatility is zero. This theoretical result is proved rigorously in this article. The outcome of an empirical study complementing the theoretical result is discussed at the end of the article. European call options are valued with the rational lognormal model and a comparably calibrated mean reverting Gaussian model. unsurprisingly, rational lognormal option values are considerably lower than the analogous mean reverting Gaussian option values. In other words, the volatility in the rational lognormal model declines so quickly that options are severely undervalued.
