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8 papers · 1 filter
A logarithm law for nonautonomous systems fastly converging to equilibrium and mean field coupled systems
Stefano Galatolo, Davide Faranda
We prove that if a nonautonomous system has in a certain sense a fast convergence to equilibrium (faster than any power law behavior) then the time needed for a typica…
Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors
Akim Viennet, Nikki Vercauteren, Maximilian Engel +1
We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discusse…
Extreme value distributions of observation recurrences
Théophile Caby, Davide Faranda, Sandro Vaienti +1
We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of…
Ruelle-Pollicott Resonances of Stochastic Systems in Reduced State Space. Part I: Theory
Mickaël Chekroun, Alexis Tantet, Henk Anton Dijkstra +1
A theory of Ruelle-Pollicott (RP) resonances for stochastic differential systems is presented. These resonances are defined as the eigenvalues of the generator (Kolmogorov operator…
Arnold maps with noise: Differentiability and non-monotonicity of the rotation number
L. Marangio, J. Sedro, S. Galatolo +2
Arnold's standard circle maps are widely used to study the quasi-periodic route to chaos and other phenomena associated with nonlinear dynamics in the presence of two rationally un…
Lagrangian reductions and integrable systems in condensed matter
François Gay-Balmaz, Michael Monastyrsky, Tudor S. Ratiu
We consider a general approach for the process of Lagrangian and Hamiltonian reduction by symmetries in chiral gauge models. This approach is used to show the complete integrabilit…