We compute accurately the golden critical invariant circles of several area-preserving twist maps of the cylinder. We define some functions related to the invariant circle and to the dynamics of the map restricted to the circle (for example, the conjugacy between the circle map giving the dynamics on the invariant circle and a rigid rotation on the circle).… (More)
CONTENTS This paper formulates some conjectures about the amplitude of 1. Introduction resonance in the General Standard Map. The main idea is to ex-2. Resonant Normal Forms pand the periodic perturbation function in Fourier series. Given 3. Rules to Determine the Resonant Normal Form any rational rotation number, we choose a finite number of har-4.… (More)
In this paper we compare diierent continuation methods for the searching of periodic orbits of the Froeschl e map, which is a four dimensional symplectic map. We nd relations between the stability of the periodic orbits and the problem to solve the system given in the continuation method.
In the last decades, renormalization group (RG) ideas have been applied to describe universal properties of different routes to chaos (quasi-periodic, period doubling or tripling, Siegel disk boundaries, etc.). Each of the RG theories leads to universal scaling exponents which are related to the action of certain RG operators. The goal of this announcement… (More)
In this work, a two-stage stochastic programming approach is implemented in a commercial simulator. A hybrid algorithm is proposed, where the first-stage decisions (existence of process units and their corresponding design parameters) are handled by a genetic algorithm, while the second-stage decisions (optimization of operational variables such as flows… (More)