# 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 CHEEMA Ammar Sabir PhD candidate +33.4.91.26.97.84 Email CORDONNIER Aurélien PhD candidate +33.4.91.26.97.85 Email Floriani Elena University faculty +33.4.91.26.95.22 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 Pettini Marco University faculty +33.4.91.26.95.49 Email Vaienti Sandro University faculty +33.4.91.26.95.44 Email Vittot Michel Researcher Chef du Groupe « Systèmes dynamiques classiques et quantiques » +33.4.91.26.95.24 Email

### List of Publications

269 results
Preprint, Working paper
A España, Xavier Leoncini, E Ugalde
Combinatorics of the paths towards synchronization
2022
Journal article
Elena Floriani, Jonathan Dubois, Cristel Chandre
Bogolyubov’s averaging theorem applied to the Kramers-Henneberger Hamiltonian
Physica D: Nonlinear Phenomena, Elsevier, 2022, 431, pp.133124. ⟨10.1016/j.physd.2021.133124⟩
Journal article
Gabriele Paolini, Francesco Sarnari, Riccardo Meucci, Stefano Euzzor, Santi Chillemi, Leone Fronzoni, Fortunato Tito Arecchi, Angelo Di Garbo, Jean-Marc Ginoux
A Fast Method for Detecting Interdependence between Time Series and Its Directionality
International journal of bifurcation and chaos in applied sciences and engineering , World Scientific Publishing, 2021, 31 (16), pp.2150239. ⟨10.1142/S0218127421502394⟩
Preprint, Working paper
Loris Cairano, Riccardo Capelli, Ghofrane Bel-Hadj-Aissa, Pettini Marco
Topological origin of protein folding transition
2021
Journal article
Arthur Vesperini, Roberto Franzosi, Stefano Ruffo, Andrea Trombettoni, Xavier Leoncini
Fast collective oscillations and clustering phenomena in an antiferromagnetic mean-field model
Chaos, Solitons and Fractals, Elsevier, 2021, 153 (2), pp.111487. ⟨10.1016/j.chaos.2021.111487⟩
Journal article
Jean-Marc Ginoux, Riccardo Meucci, Stefano Euzzor, Angelo Di Garbo
Torus breakdown in a two-stroke relaxation memristor
Chaos, Solitons and Fractals, Elsevier, 2021, 153 (2), pp.111594. ⟨10.1016/j.chaos.2021.111594⟩
Preprint, Working paper
Matteo Gori, Roberto Franzosi, Giulio Pettini, Pettini Marco
Topological Theory of Phase Transitions
2021
Journal article
Loris Di Cairano, Matteo Gori, Marco Pettini
Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
Entropy, MDPI, 2021, 23 (11), pp.1414. ⟨10.3390/e23111414⟩
Preprint, Working paper
Sandro Vaienti, Sandro Gallo, Nicolai Haydn
Number of visits in arbitrary sets for $\phi$-mixing dynamics
2021
Preprint, Working paper
Sandro Vaienti, Jason Atnip, Gary Froyland, Cecilia González-Tokman
Equilibrium states for non-transitive random open and closed dynamical systems
2021
269 results

May 2022 :