# 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

 Asch Joachim University faculty +33.4.91.26.95.20 Email Aschbacher Walter University faculty +33.4.91.26.95.16 Email Bui Olivier PhD candidate Email Caby Théophile PhD candidate Email Delliaux Stéphane Guest Email ESPANA Andrea PhD candidate Email Floriani Elena University faculty +33.4.91.26.95.22 Email Gori Matteo Postdoctoral researcher Email Lechelon Mathias Postdoctoral researcher Email Leoncini Xavier University faculty Référent pôle de recherche interdisciplinaire et intersectoriel AMU - Energie Chef de l’équipe « Systèmes dynamiques : théories et applications » +33.4.91.26.95.38 Email Maestri Stefano PhD candidate Email Pettini Marco University faculty +33.4.91.26.95.24 Email Vaienti Sandro University faculty +33.4.91.26.95.44 Email Valvo Lorenzo PhD candidate Email Vittot Michel Researcher Chef du Groupe « Systèmes dynamiques classiques et quantiques » +33.4.91.26.95.24 Email Wang Tianbo PhD candidate Email

### List of Publications

209 results
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
Huyi Hu, Sandro Vaienti
Lower Bounds for the Decay of Correlations in Non-uniformly Expanding Maps
Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), In press, ⟨10.1017/etds.2017.107⟩
Journal article
Giorgio Turchetti, S. Sinigardi, G. Servizi, Federico Panichi, 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
D. Grasso, E. Tassi, H. M. Abdelhamid, P. J. Morrison
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⟩
Journal article
Gilles Chabriel, Ghislain Gassier, Jean Barrere, Francoise Briolle, Claude Jauffret
A Unifying Approach for Disturbance Cancellation and Target Detection in Passive Radar Using OFDM
IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2016, 64 (22), pp.5959 - 5971. ⟨10.1109/TSP.2016.2600511⟩
Journal article
Francesco Fedele, Cristel Chandre, Mohammad Farazmand
Kinematics of fluid particles on the sea surface. 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⟩
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
209 results

June 2019 :