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The term non-linear or nonlinear has several definitions but is generally used to describe a system that cannot be approximated by a superposition principle or perturbative approach.
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Chaos implies Nonlinearity?
Why, for finite dimensions, is nonlinearity a precondition for chaos?
This article (Linear Chaos? By Nathan S. Feldman) offers an example of an infinite dimensional chaotic map, which is linear. Whi …