Related papers: Lyapunov exponents in 1d disordered system with lo…
Consider a non-autonomous continuous-time linear system in which the time-dependent matrix determining the dynamics is piecewise constant and takes finitely many values $A_1, \dotsc, A_N$. This paper studies the equality cases between the…
We observe a singularity in the electronic properties of the Anderson Model of Localization with bounded diagonal disorder, which is clearly distinct from the well-established mobility edge (localization-delocalization transition) that…
We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment…
Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We…
We analyze the scaling behavior of the two smallest Lyapunov exponents for electrons propagating on two-dimensional lattices with energies within a very narrow interval around the chiral critical point at E=0 in the presence of a…
We consider a disordered one-dimensional tight-binding model with power-law decaying hopping amplitudes to disclose wavefunction maximum distributions related to the Anderson localization phenomenon. Deeply in the regime of extended states,…
We study products of arbitrary random real $2 \times 2$ matrices that are close to the identity matrix. Using the Iwasawa decomposition of $\text{SL}(2,{\mathbb R})$, we identify a continuum regime where the mean values and the covariances…
In this article, we consider the hyperbolic and parabolic Anderson models in arbitrary space dimension $d$, with constant initial condition, driven by a Gaussian noise which is white in time. We consider two spatial covariance structures:…
We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…
Let $X_1,X_2, \ldots $ be a sequence of $i.i.d$ real (complex) $d \times d $ invertible random matrices with common distribution $\mu$ and $\sigma_1(n), \sigma_2(n), \ldots , \sigma_d(n)$ be the singular values, $\lambda_1(n), \lambda_2(n),…
We show, using quasi-exact numerical simulations, that Anderson localization of one-dimensional particles in a disordered potential survives in the presence of attractive interaction between particles. The localization length of the…
Covariant Lyapunov vectors characterize the directions along which perturbations in dynamical systems grow. They have also been studied as predictors of critical transitions and extreme events. For many applications like, for example,…
The cumulants of the logarithm of the conductance (lng) in the localized regime in the one-dimensional Anderson model are calculated exactly in the second Born approximation for weak disorder. Only the first two cumulants turn out to ne…
We investigate localization properties of electron eigenstates in one-dimensional (1d) systems with long-range correlated diagonal disorder. Numerical studies on the localization length $\xi$ of eigenstates demonstrate the existence of the…
This work is devoted to further consideration of the Henon map with negative values of the shrinking parameter and the study of transient oscillations, multistability, and possible existence of hidden attractors. The computation of the…
A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and…
We characterize the macroscopic attractor of infinite populations of noisy maps subjected to global and strong coupling by using an expansion in order parameters. We show that for any noise amplitude there exists a large region of strong…
We consider finite and infinite-dimensional first-order consensus systems with timeconstant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual…
The exact value of the Lyapunov exponents for the random matrix product $P_N = A_N A_{N-1}...A_1$ with each $A_i = \Sigma^{1/2} G_i^{\rm c}$, where $\Sigma$ is a fixed $d \times d$ positive definite matrix and $G_i^{\rm c}$ a $d \times d$…
We consider a finite number of orientation preserving $C^2$ interval diffeomorphisms and apply them randomly in such a way that the expected Lyapunov exponents at the boundary points are positive. We prove the exponential decay of…