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# Dynamical Systems: Theory and Applications

contact : contact-DSTA@cpt.univ-mrs.fr

Nonlinear dynamical systems

Ergodic theory

Hamiltonian systems

Plasma physics

Biophysics

Statistical Properties of Dynamical Systems: Probabilistic methods are used to study limit theorems in the case of deterministic and random dynamical systems, especially the central limit theorem (CLT), the Almost Sure Invariance Principle, the large deviations and the distribution of rare events.

The rate of decay of correlations for non-uniformly hyperbolic systems is estimated through new techniques (coupling, renewal). Random systems (by random composition of maps acting on the same space) and sequential dynamical systems (non-stationary, or non-autonomous, processes where a concatenation of maps act on a space) are also studied. We have formulated and develop the extreme value theory for random and non-autonomous systems and with the extension to coupled map lattices.

Fusion plasma physics : We develop reduced Hamiltonian fluid and kinetic models from Dirac’s constraint theory to investigate fundamental mechanisms of turbulent magnetized plasma that deteriorate the confinement in tokamak devices. Spurious instabilities in non-Hamiltonian hybrid model for interaction of energetic particles with a thermal plasma are also investigated, as well as

secondary instabilities following magnetic reconnection. Another part of the research activity concerns the application of the theory of stochastic processes to study the formation of transport barriers in tokamaks.

Biophysics : We focus on the fundamental physical processes, in particular resonant electrodynamic forces acting at a long distance, which are surmised to be responsible of the high efficiency of the molecular machinery within living cells and long-range coherence in biological systems. This activity is pursued on both theoretical and experimental sides in collaboration with molecular biologists.

Complexity: New methods of measuring networks complexity are developed within the framework of Riemannian Information Geometry. Applications to protein interaction networks in cancer cells are being developed.