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Nonexpansive Uniformly Asymptotically Stable Flows are Linear
Published online by Cambridge University Press: 20 November 2018
Abstract
We show that if a flow (R, X, π) on a separable metric space (X, d) satisfies (i) the transition mapping π(t, •): X → X is non-expansive for every t ≥ 0; (ii) X contains a globally uniformly asymptotically stable compact invariant subset, then the flow (R, X, π) is linear in the sense that it can be topologically and equivariantly embedded into a flow () on the Hilbert space l2 for which all of the transition mappings are linear operators on l2.
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- Copyright © Canadian Mathematical Society 1981
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