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
Maxime Perin, Cristel Chandre, Emanuele Tassi
Hamiltonian fluid reductions of drift-kinetic equations and the link with water-bags
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2016, 49
Journal article
Cameron Caligan, Cristel Chandre
Conservative dissipation: How important is the Jacobi identity in the dynamics?
Chaos, American Institute of Physics, 2016, 26, pp.053101. 〈10.1063/1.4948411〉
Journal article
Irene Donato, Matteo Gori, Marco Pettini, Giovanni Petri, Sarah De Nigris, Roberto Franzosi, Francesco Vaccarino
Persistent Homology analysis of Phase Transitions
Physical Review E , American Physical Society (APS), 2016, 93 (5), pp.052138 〈10.1103/PhysRevE.93.052138〉
Journal article
Matteo Gori, Irene Donato, Elena Floriani, Ilaria Nardecchia, Marco Pettini
Random walk of passive tracers among randomly moving obstacles
Theoretical Biology and Medical Modelling, BioMed Central, 2016, 13, pp.13. 〈10.1186/s12976-016-0038-1〉
Journal article
Cristel Chandre, Maxime Perin
Hamiltonian reductions of the one-dimensional Vlasov equation using phase-space moments
Journal of Mathematical Physics, American Institute of Physics (AIP), 2016, 57, pp.032902
Journal article
E Tassi
Hamiltonian reduced fluid model for plasmas with temperature and heat flux anisotropies
Theoretical and Mathematical Physics, Consultants bureau, 2016, 188 (3), pp.1377 - 1393. 〈10.1134/S0040577916090099〉
Valerio Lucarini, Davide Faranda, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Holland Mark, Kuna Tobias, Matthew Nicol, Mike Todd, Sandro Vaienti
Extremes and Recurrence in Dynamical Systems
Wiley Interscience, 2016, Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts, 9781118632192
Journal article
Davide Faranda, Jorge Milhazes Freitas, Pierre Guiraud, Sandro Vaienti
Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations
Stochastics and Dynamics, World Scientific Publishing, 2016, 16 (3), pp.1660015. 〈10.1142/S0219493716600157〉
Journal article
Elena Floriani, Ricardo Lima, Ouerdia Ourrad, Lionel Spinelli
Flux through a Markov chain
Chaos, Solitons and Fractals, Elsevier, 2016, 93, pp.136 - 146. 〈10.1016/j.chaos.2016.10.006〉
Journal article
Ana Cristina Freitas, Jorge Milhazes Freitas, Mike Todd, Sandro Vaienti
Rare Events for the Manneville-Pomeau Map
Stochastic Processes and their Applications, Elsevier, 2016, 126 (11), pp.3463-3479 〈10.1016/j.spa.2016.05.001〉
190 results