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 |
Non-commutative Tomography: Applications to Data Analysis
J. Machado, D. Baleanu, A. Luo. Discontinuity and Complexity in Physical Systems, springer, pp.215-254, 2014, nonlinear systems and complexity, 978-3-319-01410-4. (10.1007/978-3-319-01411-1__12)
On an intrinsic approach of the guiding-center anholonomy and gyro-gauge-arbitrariness
Physics of Plasmas, 2013, 20 (11), pp.112509. (10.1063/1.4831986)
Gyro-gauge-independent formulation of the guiding-center reduction to arbitrary order in the Larmor radius
Plasma Physics and Controlled Fusion, 2013, 55, pp.105001
Réductions hamiltoniennes en physique des plasmas autour de la gyrocinétique intrinsèque
Physique mathématique [math-ph]. Aix-Marseille Université, 2013. Français. (NNT : )
Casimir invariants and the Jacobi identity in Dirac's theory of constrained Hamiltonian systems
Journal of Physics A: Mathematical and Theoretical, 2013, 46, pp.375201. (10.1088/1751-8113/46/37/375201)
A gyro-gauge independent minimal guiding-center reduction by Lie-transforming the velocity vector field
Physics of Plasmas, 2013, 20, pp.082505
Self-regulation of turbulence bursts and transport barriers
Plasma Physics and Controlled Fusion, 2013, 55 (9), pp.095012. (10.1088/0741-3335/55/9/095012)
Critical behaviour of the XY -rotors model on regular and small world networks
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015], 2013, 88 (1), pp.012131. (10.1103/PhysRevE.88.012131)
Fronts between periodic patterns for bistable recursions on lattices
Journal of Dynamics and Differential Equations, 2013, 25, pp.17-31. (10.1007/s10884-012-9285-y)
Extreme Values and Recurrence for Deterministic and Stochastic Dynamics
General Mathematics [math.GM]. Université de Toulon; Universidade do Porto. Faculdade de ciências, 2013. English. (NNT : 2013TOUL0006)
