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Local Lyapunov exponents computed from observed data. (English) Zbl 0802.58041
The Lyapunov exponents of a dynamical system quantify the growth or decay of infinitesimal perturbations to orbits of that system, the long-time growth rates refer to invariants of the dynamical system (standard exponents, named global). The paper develops the authors’ earlier introduced notion [ibid. 1, No. 2, 175-199 (1991; Zbl 0797.58053)] of local Lyapunov exponents, which determine how a perturbation to a system orbit will grow in a finite time. The local exponents are shown to be derivable from observations of a scalar data set (e.g. a reconstruction of the dynamics from an experimental signal enters the scene). In several examples like Hénon map, Lorenz system, Ikeda map, it is demonstrated that the method allows one to accurately reproduce results determined when the dynamics is known beforehand.

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI
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