Group “Classical and Quantum Dynamical Systems”
Statistical properties of dynamical systems: Probabilistic methods are used to study limit theorems in the case of deterministic and random dynamical systems, in particular the Central Limit Theorem (CLT), the Almost Sure Invariance Principle, large deviations, and the distribution of rare events. The rate of decay of correlations for non-uniformly hyperbolic systems is estimated using new techniques (coupling, renewal). Random systems (by random composition of mappings acting on the same space) and sequential dynamical systems (non-stationary or non-autonomous, where a concatenation of mappings acts on a space) are also studied. We have formulated and developed the theory of extreme values for random and non-autonomous systems, with extensions to networks of coupled mappings.
Fusion plasma physics: We develop reduced fluid and kinetic Hamiltonian models derived from Dirac’s constraint theory to study the fundamental mechanisms of turbulent magnetized plasmas that degrade confinement in tokamak devices. Parasitic instabilities in a hybrid non-Hamiltonian model for the interaction of energetic particles with a thermal plasma are also studied, as well as secondary instabilities following magnetic reconnection. Another part of the research activity concerns the application of stochastic process theory to study the formation of transport barriers in tokamaks.
Biophysics: We focus on fundamental physical processes, in particular resonant electrodynamic forces acting over long distances, which are thought to be responsible for the high efficiency of molecular machinery within living cells and for long-range coherence in biological systems. This activity is pursued both theoretically and experimentally in collaboration with molecular biologists.
Complexity: New methods for measuring the complexity of networks are developed within the framework of Riemannian Information Geometry. Applications to networks of proteomic interactions in cancer cells are currently being developed.
| ASCH | Joachim | Research teacher | +33.4.91.26.95.20 | Contact |
| ASCHBACHER | Walter | Research teacher | +33.4.91.26.95.16 | Contact |
| DAQUIN | Jerome | Research teacher | Contact | |
| EL KETTANI | Perla | Research teacher Unit leader « Systèmes dynamiques classiques et quantiques » | +33.4.91.26.97.93 | Contact |
| FLORIANI | Elena | Research teacher | +33.4.91.26.95.22 | Contact |
| LEBOUAZDA | Yohann | Ph.D. | Contact | |
| LEONCINI | Xavier | Research teacher Team leader « Dynamical Systems: Theory and Applications » | +33.4.91.26.95.38 | Contact |
| PETTINI | Marco | Research teacher | +33.4.91.26.95.49 | Contact |
| ROUVET | Simon | Ph.D. | Contact | |
| VAIENTI | Sandro | Research teacher | +33.4.91.26.95.44 | Contact |
| VITTOT | Michel | Researcher | +33.4.91.26.95.24 | Contact |
Probabilistic aspects of dynamical systems
Chaos, Solitons & Fractals, 2020, 133, pp.109654. (10.1016/j.chaos.2020.109654)
Extreme value theory of evolving phenomena in complex dynamical systems: Firing cascades in a model of a neural network
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020, 30 (4), pp.043118. (10.1063/1.5120570)
On the Computation of the Extremal Index for Time Series
Journal of Statistical Physics, 2020, 179 (5-6), pp.1666-1697. (10.1007/s10955-019-02423-z)
A spectral approach for quenched limit theorems for random hyperbolic dynamical systems
Transactions of the American Mathematical Society, 2020, 373 (1), pp.629-664. (10.1090/tran/7943)
Extreme value theory for dynamical systems, with applications in climate and neuroscience
Dynamical Systems [math.DS]. Université de Toulon; Università degli studi dell' Insubria (Come, Italie). Facolta' scienze matematiche, fisiche e naturali, 2019. English. (NNT : 2019TOUL0017)
Théorie mathématique du transport topologique dans des modèles unitaires sur réseaux
Physique mathématique [math-ph]. Université de Toulon; Ecole nationale d'enseignement supérieur des Comores, 2019. Français. (NNT : 2019TOUL0015)
Hamiltonian Perturbation Theory on a Poisson Algebra. Application to a Throbbing Top and to Magnetically Confined Particles
Mathematical Physics [math-ph]. Aix Marseille University, 2019. English. (NNT : )
Propriétés statistiques des réseaux des applications couplées et récurrence des applications des dendrites locales
Systèmes dynamiques [math.DS]. Université de Toulon; Université de Sfax (Tunisie), 2019. Français. (NNT : 2019TOUL0019)
Generalized dimensions, large deviations and the distribution of rare events
Physica D: Nonlinear Phenomena, 2019, 400, pp.132143. (10.1016/j.physd.2019.06.009)
Coherent Riemannian-geometric description of Hamiltonian order and chaos with Jacobi metric
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019, 29 (12), pp.123134. (10.1063/1.5119797)
