We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperboli...

We study the Lyapunov instability of a three-dimensional fluid composed of rigid diatomic molecules by molecular dynamics simulation. We use center-of-mass coordinates and angular variables for the configurational space variables. The spectra of Lyapunov exponents are obtained for 32 rigid diatomic molecules interacting through the Weeks-Chandler-Andersen potential for various bond lengths and ...

We show that Lyapunov exponents of a stochastic system, when computed for a specific realization of the noise process, are related to conditional Lyapunov exponents in deterministic systems. We propose to use the term stochastically induced regularity instead of noise-induced synchronization and explain the reason why. The nature of stochastically induced regularity is discussed: in some instan...

Abstract. We analyze the Lyapunov exponents of U(1) gauge fields across the phase transition from the confinement to the Coulomb phase on the lattice which are initialized by quantum Monte Carlo simulations. We observe all features of a strange attractor with a tendency to regularity towards the continuum limit. Results are also displayed for the full spectrum of Lyapunov exponents of the SU(2)...

It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory, we derive numerical and in particular, analytical results that provide insights into the overall behavior of the Lyapunov exponents particularly for strange attractors. The corresponding distri...

This book provides a systematic introduction to smooth ergodic theory, including the general theory of Lyapunov exponents, nonuniform hyperbolic theory, stable manifold theory emphasizing absolute continuity of invariant foliations, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The book can be used as a primary textbook for a special topics course on nonuniform hy...

An ordinary differential equations (ODE) system describing the oscillation dynamics of a neuronal network is numerically integrated aiming to evidence chaos by the change in sign from negative to positive of the maximum Lyapunov exponents, and by a sudden decrease in the error doubling time. The error doubling time is calculated for different frequencies of the spiking rate oscillations. Than, ...

In this paper we use a path-integral approach to represent the Lyapunov exponents of both deterministic and stochastic dynamical systems. In both cases the relevant correlation functions are obtained from a (one-dimensional) supersymmetric field theory whose Hamil-tonian, in the deterministic case, coincides with the Lie-derivative of the associated Hamil-tonian flow. The generalized Lyapunov e...

We describe the statistical properties of growth rates of a linear oscillator driven by a parametric noise. We show that in general the fluctuations of local Lyapunov exponents are non-Gaussian and demonstrate multiscaling. Analytical calculations of the generalized Lyapunov exponents are complemented with approximative and numerical results; this allows us to identify the parameter range where...

We study the existence or nonexistence of true trajectories of chaotic dynamical systems that lie close to computer-generated trajectories. The nonexistence of such shadowing trajectories is caused by finite-time Lyapunov exponents of the system fluctuating about zero. A dynamical mechanism of the unshadowability is explained through a theoretical model and identified in simulations of a typica...