Chaotic dynamics in a flexible exchange rate system: a study of noise effects.
We consider two characteristic exponents of a rational function f:ℂ̂ → ℂ̂ of degree d ≥ 2. The exponent is the average of log∥f’∥ with respect to the measure of maximal entropy. The exponent can be defined as the maximal characteristic exponent over all periodic orbits of f. We prove that if and only if f(z) is conformally conjugate to .
In this paper we extend results of Blokh, Bruckner, Humke and Sm’ıtal [Trans. Amer. Math. Soc. 348 (1996), 1357–1372] about characterization of -limit sets from the class of continuous maps of the interval to the class of continuous maps of the circle. Among others we give geometric characterization of -limit sets and then we prove that the family of -limit sets is closed with respect to the Hausdorff metric.
We classify the phase portraits of the cubic systems in the plane such that they do not have finite critical points, and the critical points on the equator of the Poincaré sphere are isolated and have linear part non-identically zero.
La classe de Maslov, classe de cohomologie entière de degré 1, définie sur un fibré vectoriel symplectique muni de deux champs de plans lagrangiens, est une obstruction à leur transversalité. L’objet de ce travail est de construire explicitement, en termes de formes différentielles, des obstructions cohomologiques analogues (de degré supérieur). On étudie de ce point de vue les sous-variétés lagrangiennes de .