Angel Jorba

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We explore different two-parametric families of quasi-periodically Forced Logistic Maps looking for universality and self-similarity properties. In the bifurcation diagram of the one-dimensional Logistic Map, it is well known that there exist parameter values s n where the 2 n-periodic orbit is superattracting. Moreover, these parameter values lay between(More)
This paper deals with the eective computation of normal forms, centre mani-folds and rst integrals in Hamiltonian mechanics. These kind of calculations are very useful since they allow, for instance, to give explicit estimates on the diu-sion time or to compute invariant tori. The approach presented here is based on using algebraic manipulation for the(More)
The purpose of this paper is to make an explicit analysis of the nonlinear dynamics around a two-dimensional invariant torus of an analytic Hamiltonian system. The study is based on normal form techniques and the computation of an approximated first integral around the torus. One of the main novel aspects of the current work is the implementation of the(More)
We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes(More)
In this paper, a review of methods for the solution of general bidiagonal systems of equations is done. Gaussian Elimination, the <italic>r</italic>-Cyclic Reduction family of algorithms and the Divide and Conquer algorithm are analyzed. A unified view of the three types of methods is proposed. The work is focussed on two basic aspects of the methods:(More)