5,315 research outputs found
Superdiffusion in the Dissipative Standard Map
We consider transport properties of the chaotic (strange) attractor along
unfolded trajectories of the dissipative standard map. It is shown that the
diffusion process is normal except of the cases when a control parameter is
close to some special values that correspond to the ballistic mode dynamics.
Diffusion near the related crisises is anomalous and non-uniform in time: there
are large time intervals during which the transport is normal or ballistic, or
even superballistic. The anomalous superdiffusion seems to be caused by
stickiness of trajectories to a non-chaotic and nowhere dense invariant Cantor
set that plays a similar role as cantori in Hamiltonian chaos. We provide a
numerical example of such a sticky set. Distribution function on the sticky set
almost coincides with the distribution function (SRB measure) of the chaotic
attractor.Comment: 10 Figure
Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos
We consider a chain of nonlinear oscillators with long-range interaction of
the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha
<2. In the continues limit the system's dynamics is described by the
Ginzburg-Landau equation with complex coefficients. Such a system has a new
parameter alpha that is responsible for the complexity of the medium and that
strongly influences possible regimes of the dynamics. We study different
spatial-temporal patterns of the dynamics depending on alpha and show
transitions from synchronization of the motion to broad-spectrum oscillations
and to chaos.Comment: 22 pages, 10 figure
Statistics of real eigenvalues in Ginibre's Ensemble of random real matrices
The integrable structure of Ginibre's orthogonal ensemble of random matrices is looked at through the prism of the probability pn,k to find exactly k real eigenvalues in the spectrum of an n×n real asymmetric Gaussian random matrix. The exact solution for the probability function pn,k is presented, and its remarkable connection to the theory of symmetric functions is revealed. An extension of the Dyson integration theorem is a key ingredient of the theory presented
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