Related papers: Cauchy distributions for the integrable standard m…

Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial satellites, leading them to migration of orbits, resonant…

We study the global boundedness of the solutions of a non-smooth forced oscillator with a periodic and real analytic forcing. We show that the impact map associated with this discontinuous equation becomes a real analytic and exact…

We address the question of representativeness of a single long unstable periodic orbit for properties of the chaotic attractor it is embedded in. Y. Saiki and M. Yamada [Phys. Rev. E 79, 015201(R) (2009)] have recently suggested the…

A sudden change of the Hamiltonian parameter drives a quantum system out of equilibrium. For a finite-size system, expectations of observables start fluctuating in time without converging to a precise limit. A new equilibrium state emerges…

We consider the incompressible Euler equations in $R^2$ when the initial vorticity is bounded, radially symmetric and non-increasing in the radial direction. Such a radial distribution is stationary, and we show that the monotonicity…

Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…

We examine isotropic and anisotropic random walks which begin on the surface of linear ($N$), square ($N \times N$), or cubic ($N \times N \times N$) lattices and end upon encountering the surface again. The mean length of walks is equal to…

We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the…

We are concerned with the Cauchy problem for the KdV equation for nonsmooth locally integrable initial profiles q's which are, in a certain sense, essentially bounded from below and q(x)=O(e^{-cx^{{\epsilon}}}),x\rightarrow+\infty, with…

Consider $G=\SL_{ d }(\mathbb R)$ and $ \Gamma=\SL_{ d }(\mathbb Z)$. It was recently shown by the second-named author \cite{s} that for some diagonal subgroups $\{g_t\}\subset G$ and unipotent subgroups $U\subset G$, $g_t$-trajectories of…

We present a quantitative version of Bilu's theorem on the limit distribution of Galois orbits of sequences of points of small height in the $N$-dimensional algebraic torus. Our result gives, for a given point, an explicit bound for the…

We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhibit very interesting time-evolving…

We consider a one-parameter family of invertible maps of a two-dimensional lattice, obtained by applying round-off to planar rotations. All orbits of these maps are conjectured to be periodic. We let the angle of rotation approach pi/2, and…

We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…

We deal with the orbit determination problem for a class of maps of the cylinder generalizing the Chirikov standard map. The problem consists of determining the initial conditions and other parameters of an orbit from some observations. A…

We consider two quenched, chiral ensembles which are coupled in such a way that a combined chiral symmetry is preserved. The coupling also links the topology of the two systems such that the number of exact zero modes in the coupled system…

In this paper, we are concerned with the Cauchy problem of the generalized surface quasi-geostrophic (SQG) equation in which the velocity field is expressed as $u=K\ast\omega$, where $\omega=\omega(x,t)$ is an unknown function and…

In this paper we present and illustrate a general methodology to apply KAM theory in particular problems, based on an {\em a posteriori} approach. We focus on the existence of real-analytic quasi-periodic Lagrangian invariant tori for…

The transition from quasiperiodicity to chaos is studied in a two-dimensional dissipative map with the inverse golden mean rotation number. On the basis of a decimation scheme, it is argued that the (minimal) slope of the critical iterated…

We have recently presented strong evidence that chaotic orbits that obey one isolating integral besides energy exist in a toy Hamiltonian model with three degrees of freedom and are bounded by regular orbits that isolate them from the…