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
Conference paper
Cristel Chandre, Michel Vittot, Guido Ciraolo
Local control of area-preserving maps
C. Chandre, X. Leoncini, G. Zaslavsky. Chaos, Complexity and Transport: Theory and Applications, Jun 2007, Marseille, France. World Scientific, pp.136, 2008
Journal article
Cristel Chandre
Réduction du chaos hamiltonien
Images de la Physique, 2007, 2006, pp.54
Journal article
Xavier Leoncini, Olivier Agullo, Magali Muraglia, Cristel Chandre
From chaos of lines to Lagrangian structures in flux conservative fields
European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2006, 53, pp.351-360. 〈10.1140/epjb/e2006-00390-7〉
Journal article
Yueheng Lan, Cristel Chandre, Predrag Cvitanovic
Variational method for locating invariant tori
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2006, 74 (4), pp.046206. 〈10.1103/PhysRevE.74.046206〉
Journal article
Elena Shchekinova, Cristel Chandre, Turgay Uzer
Phase space structures and ionization dynamics of hydrogen atom in elliptically polarized microwaves
Physical Review A, American Physical Society, 2006, 74, pp.043417. 〈10.1103/PhysRevA.74.043417〉
Journal article
Cristel Chandre, Guido Ciraolo, Ricardo Lima, Michel Vittot
Contrôle du chaos Hamiltonien et amélioration du confinement dans les plasmas de fusion magnétique
Bulletin de la FRUMAM, 2006, 6, pp.6
Journal article
Cristel Chandre, Turgay Uzer
Instantaneous frequencies of a chaotic system
Pramana - Journal of Physics, Indian Academy of Sciences/Springer, 2005, 64, pp.371
Journal article
Elena Shchekinova, Cristel Chandre, Yueheng Lan, Turgay Uzer
Analyzing intramolecular dynamics by Fast Lyapunov Indicators
Journal of Chemical Physics, American Institute of Physics, 2004, 121 (8), pp.3471. 〈10.1063/1.1756875〉
Journal article
Patrice Le Gal, Jean-Francis Ravoux, Elena Floriani, T. Dudok De Wit
Recovering coefficients of the complex Ginzburg-Landau equation from experimental spatio-temporal data: two examples from hydrodynamics
Physica D: Nonlinear Phenomena, Elsevier, 2003, 174, pp.114-133
Journal article
Elena Floriani, Dimitri Volchenkov, Ricardo Lima
A system close to a threshold of instability
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2003, 36, pp.4771-4783
202 results