MIÉRCOLES 13/12 a las 13hs:
*** Presencial: Aula 8/Seminarios (CIMA, Pab II, 2do piso) ******
Coloquio Extraordinario en el marco de las visitas de investigadores al IRL IFAECI
Taxonomy of chaotic invariant sets
Dr. Christophe Letellier – Rouen Normandie Université
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labeling. Addressing these problems corresponds to the development of a dynamical taxonomy, exhibiting the key properties discriminating the variety of chaotic behaviors discussed in the abundant literature. Starting from the hierarchy of chaos initially proposed by Otto E. Rössler, the description of chaotic regimes observed in three- and four-dimensional spaces which cover a large variety of known (and less known) examples of chaos is systematized. Starting with the spectrum of Lyapunov exponents as the first taxonomic ranks, we extended the description to higher ranks with some concepts inherited from topology
(bounding torus, surface of section, first-return map, . . . ).
The Rössler and the Lorenz attractors are described in terms of template — the highest known taxonomic rank for classifying chaotic attractor — with the help of a linking matrix (or linker) and multicomponent Poincaré sections. The expected extension with the novel concept of templex will be also discussed.
With a PhD thesis devoted to the topological characterization of chaotic attractors, Dr. Letellier developped an extended procedure for systems with symmetries. He also worked with symbolic dynamics. Involved in global modelling (machine learning), He developed a symbolic procedure to compute the observability of high-dimensional nonlinear systems and now use it to design flat control law (based on global observability and global controllability). Dr. Letellier worked for 20 years in biomedical applications (noninvasive ventilation, cardiac variability, tumor growth). Alongside, He is deeply interested in history of science.