Related papers: Stickiness in generic low-dimensional Hamiltonian …
We develop the formulation of turbulence in terms of the functional integral over the phase space configurations of the vortex cells. The phase space consists of Clebsch coordinates at the surface of the vortex cells plus the Lagrange…
We study the propagation of waves in quasi-one-dimensional finite periodic systems whose classical (ray) dynamics is diffusive. By considering a random matrix model for a chain of $L$ identical chaotic cavities, we show that its average…
In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in…
The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with…
We discuss the applicability of the Melnikov and Landau-Teller theories in obtaining semi-analytical estimates of the speed of chaotic diffusion in systems driven by the separatrix-like stochastic layers of a resonance belonging to the…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
Exploring chaotic systems via Poincar\'e sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach…
We numerically examine a binary system of particles with repulsive interactions, where one species is driven by a rotating drive and the other is subjected either to a constant drive in a fixed direction or to a rotating drive that is out…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…
The route to chaos and phase dynamics in a rotating shallow-water model were rigorously examined using a five-mode Galerkin truncated system with complex variables. This system is valuable for investigating how large/meso-scales destabilize…
The problem of synchronization of coupled Hamiltonian systems exhibits interesting features due to the non-uniform or mixed nature (regular and chaotic) of the phase space. We study these features by investigating the synchronization of…
We investigate the phase space structure and dynamics of a Hamiltonian isokinetic thermostat, for which ergodic thermostat trajectories at fixed (zero) energy generate a canonical distribution in configuration space. Model potentials…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
We study a chipping model in one dimensional periodic lattice with continuous mass, where a fixed fraction of the mass is chipped off from a site and distributed randomly among the departure site and its neighbours; the remaining mass…
We study numerically statistical distributions of sums of orbit coordinates, viewed as independent random variables in the spirit of the Central Limit Theorem, in weakly chaotic regimes associated with the excitation of the first ($k=1$)…
An algorithm for detecting unstable periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.…