Centre de Physique Théorique

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

List of Publications

202 results
Journal article
D Dragičević, G Froyland, Cecilia González-Tokman, Sandro Vaienti
Almost sure invariance principle for random piecewise expanding maps
Nonlinearity, IOP Publishing, 2018, 31 (5), pp.2252. 〈10.1088/1361-6544/aaaf4b〉
Journal article
Davide Faranda, Sandro Vaienti
Correlation dimension and phase space contraction via extreme value theory
Chaos, American Institute of Physics, 2018, 28, pp.041103. 〈10.1063/1.5027386〉
Mohamed Abdelkader
Limit theorems in the statistical analysis of dynamical systems
Mathématiques générales [math.GM]. Université de Toulon, 2017. Français. 〈NNT : 2017TOUL0010〉
Journal article
Emanuele Tassi
Hamiltonian closures in fluid models for plasmas
The European Physical Journal D, EDP Sciences, 2017, 71 (11), pp.269. 〈10.1140/epjd/e2017-80223-6〉
Journal article
Shun Ogawa
Stability criterion of spatially inhomogeneous solutions to the Vlasov equation
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2017, 50 (45), pp.455001. 〈10.1088/1751-8121/aa8dbb〉
Preprint, Working paper
Davide Faranda, H Ghoudi, P Guiraud, Sandro Vaienti
Synchronisation and Extreme Value Theory for Coupled Map Lattices
Journal article
Ilaria Nardecchia, Mathias Lechelon, Matteo Gori, Irene Donato, Jordane Preto, Elena Floriani, Sébastien Jaeger, Sébastien Mailfert, Didier Marguet, Pierre Ferrier, Marco Pettini
Detection of long-range electrostatic interactions between charged molecules by means of fluorescence correlation spectroscopy
Physical Review E , American Physical Society (APS), 2017, 96 (2), pp.022403 〈10.1103/PhysRevE.96.022403〉
Journal article
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Sandro Vaienti
Extreme Value Laws For Non Stationary Processes Generated By Sequential And Random Dynamical Systems
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2017, 53 (3), pp. 1341-1370 〈10.1214/16-AIHP757〉
Journal article
Thierry Passot, P L Sulem, Emanuele Tassi
Electron-scale reduced fluid models with gyroviscous effects
Journal of Plasma Physics, Cambridge University Press (CUP), 2017, 83 (4), pp.715830402. 〈10.1017/S0022377817000514〉
Journal article
Nicolai Haydn, Matthew Nicol, Andrew Török, Sandro Vaienti
Almost sure invariance principle for sequential and non-stationary dynamical systems
Transactions of the American Mathematical Society, American Mathematical Society, 2017, 369 (8), pp. 5293-5316 〈10.1090/tran/6812〉
202 results