Related papers: Global Superdiffusion of Weak Chaos
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
A method to predict the emergence of different kinds of ordered collective behaviors in systems of globally coupled chaotic maps is proposed. The method is based on the analogy between globally coupled maps and a map subjected to an…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
We perform an extensive and detailed analysis of the generalized diffusion processes in deterministic area preserving maps with noncompact phase space, exemplified by the standard map, with the special emphasis on understanding the…
Mixing and transport of passive particles are studied in a simple kinematic model of a meandering jet flow motivated by the problem of lateral mixing and transport in the Gulf Stream. We briefly discuss a model streamfunction, Hamiltonian…
We assume that a symplectic real-analytic map has an invariant normally hyperbolic cylinder and an associated transverse homoclinic cylinder. It is well known that such cylinder is preserved under small perturbations. We prove that for a…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…
Angle-action maps that are periodic in the action direction can have accelerator modes: orbits that are periodic when projected onto the torus, but that lift to unbounded orbits in an action variable. In this paper we construct a…
The character of motion (regular or chaotic) on the quantum level manifests itself in the statistics of the set of the system's energy levels. The completely regular case generates the sequence of the levels with exponential (Poisson) level…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
We provide numerical evidence of global diffusion occurring in slightly perturbed integrable Hamiltonian systems and symplectic maps. We show that even if a system is sufficiently close to be integrable, global diffusion occurs on a set…
Numerical simulations carried out over the past decade suggest that the orbits of the Global Navigation Satellite Systems are unstable, resulting in an apparent chaotic growth of the eccentricity. Here we show that the irregular and…
We present a detailed theory of spectacular semiclassical catastrophes happening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett. {\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems are analyzed.…
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…
Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
Recently it was found that the dynamics in a Heisenberg spin-chain subjected to a sequence of periodic pulses from an external, parabolic, magnetic field can have a close correspondence with the quantum kicked rotor (QKR). The QKR is a key…
The destruction of regular regions in two-dimensional, area-preserving maps is traditionally described in terms of the breakup of invariant curves and the persistence of transport barriers. Here, we investigate how this scenario changes…
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…