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This works investigates the Lyapunov-Oseledets spectrum of transfer operator cocycles associated to one-dimensional random paired tent maps depending on a parameter $\epsilon$, quantifying the strength of the \emph{leakage} between two…

Consider the stochastic heat equation $\partial_tu=\mathscr{L}u+\lambda\sigma(u)\xi$, where $\mathscr{L}$ denotes the generator of a L\'{e}vy process on a locally compact Hausdorff Abelian group $G$, $\sigma:\mathbf{R}\to\mathbf{R}$ is…

For the 2D matrix Langevin dynamics that corresponds to the continuous-time limit of the product of some $2 \times 2$ random matrices, the finite-time Lyapunov exponent can be written as an additive functional of the associated Riccati…

We compute the diffusion coefficient and the Lyapunov exponent for a diffusive intermittent map by means of cycle expansion of dynamical zeta functions. The asymptotic power law decay of the coefficients of the relevant power series are…

We exploit the analogy between dynamics of inertial particle pair separation in a random-in-time flow and the Anderson model of a quantum particle on the line in a spatially random real-valued potential. Thereby we get an exact formula for…

Let $u$ be a solution of the Cauchy problem for the nonlinear parabolic equation $$ \partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N, $$ and assume that the…

This paper is concerned with the integrodifferential equation $$\partial_t u-\Delta u -\int_0^\infty \kappa(s)\Delta u(t-s)\,\d s + \varphi(u)=f$$ arising in the Coleman-Gurtin's theory of heat conduction with hereditary memory, in presence…

We consider the class of long-range Hamiltonian systems first introduced by Anteneodo and Tsallis and called the alpha-XY model. This involves N classical rotators on a d-dimensional periodic lattice interacting all to all with an…

The rate function for large deviations of the finite time Lyapunov exponent for the derived process in TM corresponding to a stochastic differential equation in M is related, via the Gartner-Ellis theorem, to the p-th moment Lyapunov…

We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schr\"odinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose…

We investigate the predictability problem in dynamical systems with many degrees of freedom and a wide spectrum of temporal scales. In particular, we study the case of $3D$ turbulence at high Reynolds numbers by introducing a finite-size…

By simulating a nonequilibrium coupled map lattice that undergoes an Ising-like phase transition, we show that the Lyapunov spectrum and related dynamical quantities such as the dimension correlation length~$\xi_\delta$ are insensitive to…

According to Anderson's orthogonality catastrophe, the overlap of the $N$-particle ground states of a free Fermi gas with and without an (electric) potential decays in the thermodynamic limit. For the finite one-dimensional system various…

We present an asymptotic approach towards the standard Landau-Zener problem based on two linearly independent elementary waves of constant amplitude but time-dependent phase. The two contributions to this phase are quadratic and logarithmic…

We consider the continuum limit of some products of random matrices in $\text{SL}(d,{\mathbb R})$ that arise as discretisations of incompressible renewing flows -- that is, of flows corresponding to a divergence-free velocity field that…

We continue the analysis of the two-phase free boundary problems initiated in \cite{DK}, where we studied the linear growth of minimizers in a Bernoulli type free boundary problem at the non-flat points and the related regularity of free…

In this paper, we study the asymptotic behavior of least energy nodal solutions $u_p(x)$ to the following fourth-order elliptic problem \[ \begin{cases} \Delta^2 u =|u|^{p-1}u \quad &\hbox{in}\;\Omega, \\ u=\frac{\partial u}{\partial \nu}=0…

Our focus is on the fast diffusion equation driven by the $p$-Laplacian operator, that is $\partial_t u=\Delta_p u$ with $1<p<2$, posed in the whole space $\mathbb{R}^N$, $N\geq 2$. The nonnegative solutions are expected to converge in time…

We study the isentropic Euler equations with time-dependent damping, given by $\frac{\mu}{(1+t)^\lambda}\rho u$. Here, $\lambda,\mu$ are two non-negative constants to describe the decay rate of damping with respect to time. We will…

Let $\Omega$ be a smooth, bounded domain of $\mathbb{R}^{N}$, $\omega$ be a positive, $L^{1}$-normalized function, and $0<s<1<p.$ We study the asymptotic behavior, as $p\rightarrow\infty,$ of the pair $\left( \sqrt[p]{\Lambda_{p}%…