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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Ghoudi Hamza PhD candidate
Leoncini Xavier University faculty
Référent pôle de recherche interdisciplinaire et intersectoriel AMU - Energie
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Maestri Stefano PhD candidate
Pettini Marco University faculty
Chef de l’équipe « Systèmes dynamiques : théories et applications »
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Rejeiba Tarek PhD candidate
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

190 results
Journal article
Alex Blumenthal, Bastien Fernandez
Population Dynamics of Globally Coupled Degrade-and-Fire Oscillators
Journal of Dynamics and Differential Equations, Springer Verlag, 2017, 29 (2), pp.523-547. 〈10.1007/s10884-015-9449-7〉
Journal article
T Kuna, Sandro Vaienti
Mathematics for the fluid earth PREFACE
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2017, 50 (17), pp.170301. 〈10.1088/1751-8121/aa639b〉
Journal article
Giorgio Turchetti, Panichi Federico, Sinigardi S., Servizi G., Sandro Vaienti
Errors, Correlations and Fidelity for noisy Hamilton flows. Theory and numerical examples
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2017, 50 (6), pp.064001. 〈10.1088/1751-8121/aa5192〉
Journal article
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Sandro Vaienti
Extreme Value Laws for Sequences of Intermittent Maps
Proceedings of the American Mathematical Society, American Mathematical Society, 2017, 〈10.1090/proc/13892〉
Journal article
E. Tassi, H. M. Abdelhamid, P. J. Morrison, D. Grasso
Structure and computation of two-dimensional incompressible extended MHD
Physics of Plasmas, American Institute of Physics, 2017, 24 (1), pp.012110 〈10.1063/1.4974039〉
Journal article
Martin Belger, Sarah De Nigris, Xavier Leoncini
Slowing down of so-called chaotic states: ``Freezing'' the initial state
Discontinuity, Nonlinearity, and Complexity, L & H Scientific Publishing, 2016, 5 (4), pp.447-455. 〈https://lhscientificpublishing.com/journals/DNC-Default.aspx〉. 〈10.5890/DNC.2016.12.009〉
Preprint, Working paper
D Dragičević, G Froyland, Cecilia González-Tokman, Sandro Vaienti
Almost sure invariance principle for random piecewise expanding maps
Journal article
Francesco Fedele, Cristel Chandre, Mohammad Farazmand
Kinematics of fluid particles on the sea surface. Part 1. Hamiltonian theory
Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016, 801, pp.260. 〈10.1017/jfm.2016.453〉
Journal article
Mark Demers, Bastien Fernandez
Escape Rates and Singular Limiting Distributions for Intermittent Maps with Holes
Transactions of the American Mathematical Society, American Mathematical Society, 2016, 368 (7), pp.4907-4932. 〈10.1090/tran/6481〉
Journal article
Roberto Franzosi, Domenico Felice, Stefano Mancini, Marco Pettini
Riemannian-geometric entropy for measuring network complexity
Physical Review E , American Physical Society (APS), 2016, 〈10.1103/PhysRevE.93.062317〉
190 results