Title:
Noise is your friend, or: How well can we resolve state space?
Noise is your friend, or: How well can we resolve state space?
Author(s)
Cvitanović, Predrag
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Abstract
All physical systems are affected by some noise that limits the resolution
that can be attained in partitioning their state space. What is the best
resolution possible for a given physical system?
It turns out that for nonlinear dynamical systems the noise itself is highly
nonlinear, with the effective noise different for different regions of
system's state space. The best obtainable resolution thus depends on the
observed state, the interplay of local stretching/contraction with the
smearing due to noise, as
well as the memory of its previous states. We show how that is computed,
orbit by orbit. But noise also associates to each orbit a finite state space
volume, thus helping us by both smoothing out what is deterministically a
fractal strange attractor, and restricting the computation to a set of
unstable periodic orbits of finite period. By computing the local
eigenfunctions of the Fokker-Planck evolution operator, forward operator
along stable linearized directions and the adjoint operator along the
unstable directions, we determine the `finest attainable' partition for a
given hyperbolic dynamical system and a given weak additive noise. The space
of all chaotic spatiotemporal states is infinite, but noise kindly
coarse-grains it into a finite set of resolvable states.
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Date Issued
2014-09-05
Extent
54:47 minutes
Resource Type
Moving Image
Resource Subtype
Lecture