Related papers: Perturbation d'un hamiltonien partiellement hyperb…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous…
Diffusion of electrons in three dimensional disordered systems is investigated numerically for all the three universality classes, namely, orthogonal, unitary and symplectic ensembles. The second moment of the wave packet $<\vv{r}^2(t)>$ at…
We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs. Under certain genericity assumptions it is proved that any bihamiltonian perturbation…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We consider the damped hyperbolic motion of polygons by a linear semi-discrete analogue of polyharmonic curve diffusion. We show that such flows may transition any polygon to any other polygon, reminiscent of the Yau problem of evolving one…
We discuss certain kinds of diffusions on hyperbolic spaces, associated random walks on discrete groups of isometries of the latter, and their Martin boundaries.
We define Landau quasi-particles within the Gutzwiller variational theory, and derive their dispersion relation for general multi-band Hubbard models in the limit of large spatial dimensions D. Thereby we reproduce our previous calculations…
This work is an extended version of the paper arXiv:0803.2669v1[math-ph], in which the main results were announced. We consider certain classical diffusion process for a wave function on the phase space. It is shown that at the time of…
We call a partially hyperbolic diffeomorphism \emph{partially volume expanding} if the Jacobian restricted to any hyperplane that contains the unstable bundle $E^u$ is larger than $1$. This is a $C^1$ open property. We show that any…
Numerical simulations of dispersive turbulence in magnetized plasmas based on the Hall-MHD description are presented, assuming spatial variations along a unique direction making a prescribed angle with the ambient magnetic field. Main…
The aim of this paper is to study the semi-classical behaviour of Schr\"odinger's dynamics for an one-dimesional quantum Hamiltonian with a classical hyperbolic trajectory. As in the regular case (elliptic trajectory), we prove, that for an…
In this paper, we prove that the net of transition chain is $\delta$-dense for nearly integrable positive definite Hamiltonian systems with 3 degrees of freedom in the cusp-residual generic sense in $C^r$-topology, $r\ge 6$. The main…
In this letter we consider the phase diffusion of a harmonically driven undamped pendulum and show that it is anomalous in the strong sense. The role played by the fractal properties of the phase space is highlighted, providing an…
We study the problem of Arnold's diffusion in an example of isochronous system by using a geometrical method known as Windows Method. Despite the simple features of this example, we show that the absence of an anisochrony term leads to…
We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
In the quasi-stationary states of the Hamiltonian Mean-Field model, we numerically compute correlation functions of momenta and diffusion of angles with homogeneous initial conditions. This is an example, in a N-body Hamiltonian system, of…
We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes…
We consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times. We are dealing with generic situations where the…