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Modeling and Inverse Problems in the Presence of Uncertainty
book

Modeling and Inverse Problems in the Presence of Uncertainty

by H. T. Banks, Shuhua Hu, W. Clayton Thompson
April 2014
Intermediate to advanced content levelIntermediate to advanced
405 pages
13h
English
Chapman and Hall/CRC
Content preview from Modeling and Inverse Problems in the Presence of Uncertainty
Propagation of Uncertainty in a Continuous Time Dynamical System 279
Lemma 7.4.1 Let (Ω, F, µ) be a σ-finite measure space, and η : be
an invertible non-singular transformation (i.e., η
1
non-singular) and P be
the associated Frobenius –Perron operator. Then for every f L
1
(Ω, F, µ) we
have
P(f(x)) = f (η
1
(x))J
1
(x), (7.132)
where J(x) is the determinant of the Jacobian matrix
η(x)
x
.
Koopman operator The Koopman operator is widely used in applications,
as it can be used to describe the evolution of the observables of a system on
the phase spac e. Its definitio n is given as follows.
Definition 7.4.5 Let (Ω, F, µ) be a σ-finite measure space. If
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Publisher Resources

ISBN: 9781482206432