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Topological chaos for a class of linear models. (English) Zbl 0770.58024

In the complex Banach space \(l_ 1\) of summable sequences a dynamical system described by a linear kinetic model is considered. Involving the backward shift operator on \(l_ 1\) the authors put in evidence the chaotic behavior of the system. It is also shown that in a certain finite-dimensional invariant subspace of \(l_ 1\) an approximate finite- time manifestation of chaos can occur. Finally, a conjugacy of linear backward shift in \(l_ 1\) with Bernoulli shift is proved.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
46B45 Banach sequence spaces
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