1994

 G. Gouesbet & C. Letellier
Global vector field reconstruction by using a multivariate polynomial approximation on nets,
Physical Review E, 49 (6), 4955-4972, 1994. Online

 Abstract:
A multivariate polynomial \(L_2\)-approximation on nets is designed for global vector field reconstructions of time continuous dynamical systems. The technique is tested by investigating standard forms of the Rössler band, the Lorenz mask and a chaotic attractor produced by a simple model of thermal lens oscillations.

 L. Le Sceller, C. Letellier & G. Gouesbet
Algebraic evaluation of linking numbers of unstable periodic orbits in chaotic attractors,
Physical Review E, 49 (5), 4693-4695, 1994. Online

 Abstract
An algebraic expression for evaluation of linking numbers of unstable periodic orbits in chaotic attractor is demonstrated. An illustrating example (horseshoe dynamics) is provided.

 C. Letellier, P. Dutertre & G. Gouesbet
Characterization of the Lorenz system taking into account the equivariance of the vector field,
Physical Review E, 49 (4), 3492-3495, 1994. Online

 Abstract
We characterize the chaotic attractors of the Lorenz system associated with \(R=28\) and \(R =90\) (reduced Rayleigh number) by using a partition taking into account the equivariance of the vector field. The population of unstable periodic orbits is extracted and encoded respectively with binary and three letter symbolic dynamics. Templates are proposed for these \(R\)-values.