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Chaotic attractors of an infinite-dimensional dynamical system. (English) Zbl 1194.37052

Summary: We study the chaotic attractors of a delay differential equation. The dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of Lyapunov exponents according to a conjecture of Kaplan and Yorke. Assuming this conjecture to be valid, as the delay parameter is varied, from computations of the spectrum of Lyapunov exponents, we observe a roughly linear increase from two to twenty in the dimension, while the metric entropy remains roughly constant. These results are compared to a linear analysis, and the asymptotic behavior of the Lyapunov exponents is derived.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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