# Instability statistics and mixing rates.

@article{Artuso2009InstabilitySA, title={Instability statistics and mixing rates.}, author={Roberto Artuso and Cesar Manchein}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2009}, volume={80 3 Pt 2}, pages={ 036210 } }

We claim that looking at probability distributions of finite time largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of polynomial decay rates of time correlations and Poincaré recurrences in the-quite-delicate case of dynamical systems with weak chaotic properties.

## 27 Citations

Lyapunov statistics and mixing rates for intermittent systems.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

It is demonstrated that a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems fails for a generic class of maps of the Pomeau-Manneville type.

Correlation decay and large deviations for mixed systems

- Physics, Mathematics
- 2016

We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate…

Collapse of hierarchical phase space and mixing rates in Hamiltonian systems

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2019

Abstract We employ statistical properties of Poincare recurrences to investigate dynamical behaviors of coupled Hamiltonian maps with a mixed phase space, where sticking to regular (or resonant)…

Extensive numerical investigations on the ergodic properties of two coupled Pomeau-Manneville Maps

- Mathematics, Physics
- 2014

We present extensive numerical investigations on the ergodic properties of two identical Pomeau–Manneville maps interacting on the unit square through a diffusive linear coupling. The system exhibits…

Chaotic Hamiltonian systems: survival probability.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

New semiphenomenological arguments are presented which enable us to map the dynamical system near the chaos border onto the effective "ultrametric diffusion" on the boundary of a treelike space with hierarchically organized transition rates.

Anomalous Diffusion: Deterministic and Stochastic Perspectives

- Mathematics
- 2014

Normal diffusion arises in a natural way from random walks with uncorrelated steps of bounded variance, or, in the deterministic setting, from wandering trajectories of a chaotic map. There are many…

Intermittent stickiness synchronization.

- Medicine, PhysicsPhysical review. E
- 2019

This work uses the statistical properties of finite-time Lyapunov exponents (FTLEs) to investigate the intermittent stickiness synchronization (ISS) observed in the mixed phase space of high-dimensional Hamiltonian systems and obtains remarkable evidence about the existence of a universal behavior related to the decay of time correlations encoded in such exponents.

Characterizing the dynamics of higher dimensional nonintegrable conservative systems.

- Mathematics, MedicineChaos
- 2012

To detect stickiness, four different measures are used, related to the distributions of the positive FTLEs, and provide conditions to characterize the dynamics, and results show that all four statistical measures sensitively characterize the motion in high dimensional systems.

Lagrangian chaos in confined two-dimensional oscillatory convection

- PhysicsJournal of Fluid Mechanics
- 2014

Abstract The chaotic advection of passive tracers in a two-dimensional confined convection flow is addressed numerically near the onset of the oscillatory regime. We investigate here a differentially…

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