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
Romain Aimino, Jérôme Rousseau
Concentration inequalities for sequential dynamical systems of the unit interval
Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2015, 〈10.1017/etds.2015.19〉
Journal article
Roberto Franzosi, Domenico Felice, Stefano Mancini, Marco Pettini
A geometric entropy detecting the Erdös-Rényi phase transition
EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2015, 111 (2), pp.20001. 〈10.1209/0295-5075/111/20001〉
Journal article
Alessio Turchi, Duccio Fanelli, Xavier Leoncini
Emergence of a collective crystal in a classical system with long-range interactions
EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2015, 111 (3), pp.30011. 〈10.1209/0295-5075/111/30011〉
Journal article
Romain Aimino, Matthew Nicol, Sandro Vaienti
Annealed and Quenched Limit Theorems for Random Expanding Dynamical Systems
Probability Theory and Related Fields, Springer Verlag, 2015, 162 (1), pp.233-274. 〈10.1007/s00440-014-0571-y〉
Journal article
G Erochenkova, Cristel Chandre
Photon plasma–wave interaction via Compton scattering
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2015, 48 (49), pp.495502. 〈10.1088/1751-8113/48/49/495502〉
Journal article
D Grasso, E Tassi
Hamiltonian magnetic reconnection with parallel electron heat flux dynamics
Journal of Plasma Physics, Cambridge University Press (CUP), 2015, 81, pp.495810501
Preprint, Working paper
Aurore Back, Eric Sonnendrücker
Conference paper
Matteo Rucco, Filippo Castiglione, Emanuela Merelli, Marco Pettini
Characterisation of the idiotypic immune network through persistent entropy
European Conference on Complex Systems (ECCS14), Sep 2014, Lucca, Italy. Springer Proceedings in Complexity, pp.117-128, 2016, Proceedings of ECCS 2014. 〈10.1007/978-3-319-29228-1_11〉
Journal article
Maxime Perin, Cristel Chandre, Philip Morrison, Emanuele Tassi
Higher order Hamiltonian fluid reduction of Vlasov equation
Annals of Physics, Elsevier Masson, 2014, 348, pp.50. 〈10.1016/j.aop.2014.05.011〉
Journal article
Emanuele Tassi
Hamiltonian structure of a drift-kinetic model and Hamiltonian closures for its two-moment fluid reductions
The European Physical Journal D, EDP Sciences, 2014, 68, pp.196
202 results