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- Frederic Gabern, Angel Jorba, Ugo Locatelli
- 2004

In this paper we focus on the stability of the Trojan asteroids for the planar Restricted Three-Body Problem (RTBP), by extending the usual techniques for the neighbourhood of an elliptic point to derive results in a larger vicinity. Our approach is based on the numerical determination of the frequencies of the asteroid and the effective computation 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)

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)

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)

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 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)

- Pablo S Casas, Angel Jorba
- 2011

This paper studies various Hopf bifurcations in the two-dimensional plane Poiseuille problem. For several values of the wavenumber α, we obtain the branch of periodic flows which are born at the Hopf bifurcation of the laminar flow. It is known that, taking α ≈ 1, the branch of periodic solutions has several Hopf bifurcations to quasi-periodic orbits. For… (More)