telech

1994 Topological characterization and global modeling of chaotic attractors

Christophe LETELLIER
29/11/2008
Christophe Letellier
Defended on May 10, 1994

I was born in 1966. I received a Bachelor degree in 1985. From 1985 to June 1989, I was involved in Physics. As a result of this work, in 1989, I received a Master’s degree in Physics from University of Rouen. In September 1990, I was involved in the DEA Champs, Particules, Matières (University of Orsay). In September 1991, I joined the CORIA as a research student for working on Topological characterization and global modelling of chaotic attractors. In May 1994, I received a PhD degree for these researches.

In September 1994, I joined the Department of Physics of the University of Rouen as a temporary assistant professor where I got a permanent position in September 1996. I got my Habilitation to Direct Researches in January 1998 and became full professor in 2007.

Abstract

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Ph.D. Thesis (DOI: 10.13140/RG.2.1.1280.5281)

Chaos theory can be applied to various domains. But in order to do that, there is a great demand to possess a better description of chaotic attractors as well as the underlying mechanisms responsible for these new types of behaviors. Such a task requires a quite theoretical approach. Roughly, two types of techniques are investigated in this Ph’D thesis: i) topological characterization and ii) global modelling. The first deals with the relative organization of unstable periodic orbits around which a chaotic attractor is structured. The original contribution of this work is to develop an appropriate way to investigate systems with symmetry property as the Lorenz system has. In particular, it is shown that there is a great advantage to modd out the symmetry property to correctly identify the relevant dynamical properties of equivariant dynamical systems. The second type technique concerns the obtention of a set of ordinary differential equations from experimental data. It is shown that it is possible to recover a set of differential equations estimated from the experimental dynamics reconstructed in a space spanned by derivative coordinates. In particular the case of noise contaminated data is solved using a smoothing procedure prior to any attempt for global modeling. In the third part of this thesis, few examples from electrochemistry and astrophysics are are investigated.

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