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Base flow (random dynamical systems)

In mathematics, the base flow of a random dynamical system is the dynamical system defined on the "noise" probability space that describes how to "fast forward" or "rewind" the noise when one wishes t

Random dynamical system

In the mathematical field of dynamical systems, a random dynamical system is a dynamical system in which the equations of motion have an element of randomness to them. Random dynamical systems are cha

Krylov–Bogolyubov theorem

In mathematics, the Krylov–Bogolyubov theorem (also known as the existence of invariant measures theorem) may refer to either of the two related fundamental theorems within the theory of dynamical sys

Absorbing set (random dynamical systems)

In mathematics, an absorbing set for a random dynamical system is a subset of the phase space. A dynamical system is a system in which a function describes the time dependence of a point in a geometri

Random compact set

In mathematics, a random compact set is essentially a compact set-valued random variable. Random compact sets are useful in the study of attractors for random dynamical systems.

Brownian motion of sol particles

Colloidal particles in a sol are continuously bombarded by the molecules of the dispersion medium on all sides. The impacts are however not equal in every direction. As a result, the sol particles sho

Pullback attractor

In mathematics, the attractor of a random dynamical system may be loosely thought of as a set to which the system evolves after a long enough time. The basic idea is the same as for a deterministic dy

Crackling noise

Crackling noise arises when a system is subject to an external force and it responds via events that appear very similar at many different scales. In a classical system there are usually two states, o

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