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Dynamical Systems: Theory and Applications

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, 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.

Directory of Members

Aschbacher Walter University faculty
+33.4.91.26.95.16 Email
Bui Olivier PhD candidate
Email
Caby Théophile PhD candidate
Email
Delliaux Stéphane Guest
Email
Floriani Elena University faculty
+33.4.91.26.95.22 Email
Gori Matteo Postdoctoral researcher
Email
Lechelon Mathias Postdoctoral researcher
Email
Leoncini Xavier University faculty
Référent pôle de recherche interdisciplinaire et intersectoriel AMU - Energie
Chef de l’équipe « Systèmes dynamiques : théories et applications »
+33.4.91.26.95.38 Email
Maestri Stefano PhD candidate
Email
Pettini Marco University faculty
+33.4.91.26.95.24 Email
Vaienti Sandro University faculty
+33.4.91.26.95.44 Email
Valvo Lorenzo PhD candidate
Email
Vittot Michel Researcher
Chef du Groupe « Systèmes dynamiques classiques et quantiques »
+33.4.91.26.95.24 Email
Wang Tianbo PhD candidate
Email

List of Publications

202 results
Journal article
Davide Faranda, Xavier Leoncini, Sandro Vaienti
Mixing properties in the advection of passive tracers via recurrences and extreme value theory
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2014, 90, pp.019902. 〈10.1103/PhysRevE.89.052901〉
Journal article
Davide Faranda, Sandro Vaienti
Extreme value laws for dynamical systems under observational noise
Physica D: Nonlinear Phenomena, Elsevier, 2014, 280-281, pp.86-94
Journal article
E Tassi
Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection
Journal of Physics: Conference Series, IOP Publishing, 2014, 561, pp.12018. 〈10.1088/1742-6596/561/1/012018〉
Journal article
W Bahsoun, H Hu, S Vaienti
Pseudo-orbits, stationary measures and metastability
Dynamical Systems, Taylor & Francis, 2014, 29 (3), pp.322-336. 〈10.1080/14689367.2014.890172〉
Journal article
Domenico Felice, Stefano Mancini, Marco Pettini
Quantifying Networks Complexity from Information Geometry Viewpoint
Journal of Mathematical Physics, American Institute of Physics (AIP), 2014, 55 (4), pp.043505. 〈10.1063/1.4870616〉
Journal article
Bastien Fernandez, Lev Tsimring
Typical trajectories of coupled degrade-and-fire oscillators: From dispersed populations to massive clustering
Journal of Mathematical Biology, Springer Verlag (Germany), 2014, 68 (7), pp.1627-1652. 〈10.1007/s00285-013-0680-8〉
Journal article
Nakia Carlevaro, Duccio Fanelli, Xavier Garbet, Philippe Ghendrih, Giovanni Montani, Marco Pettini
Beam–plasma instability and fast particles: the Lynden-Bell approach
Plasma Physics and Controlled Fusion, IOP Publishing, 2014, 56 (3), pp.035013. 〈10.1088/0741-3335/56/3/035013〉
Journal article
Loïc De Guillebon, Michel Vittot
On an intrinsic approach of the guiding-center anholonomy and gyro-gauge-arbitrariness
Physics of Plasmas, American Institute of Physics, 2013, 20 (11), pp.112509. 〈10.1063/1.4831986〉
Journal article
Loïc De Guillebon, Vittot Michel
Gyro-gauge-independent formulation of the guiding-center reduction to arbitrary order in the Larmor radius
Plasma Physics and Controlled Fusion, IOP Publishing, 2013, 55, pp.105001
Thesis
Loïc De Guillebon
Hamiltonian reductions in plasma physics about intrinsic gyrokinetics
Physique mathématique [math-ph]. Aix-Marseille Université, 2013. Français
202 results

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