منابع مشابه
Lyapunov Exponents of Symmetric Attractors
The Lyapunov exponents of symmetric attractors can be forced to be multiple by “instantaneous symmetries” which fix the attractor pointwise. In this paper, we show that “symmetries on average” which fix the attractor as a set may lead to further multiplicities. This work is motivated by, and provides an explanation for, numerical computations by Aston & Laing of Lyapunov exponents for the compl...
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in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...
15 صفحه اولLyapunov Exponents
The analysis of potentially chaotic behavior in biological and biomedical phenomena has attracted great interest in recent years (1–6). Although no universally accepted mathematical definition of the term chaos exists, Strogatz (7) provides a working definition as ‘‘aperiodic long-term behavior in a deterministic system that exhibits sensitive dependence on initial conditions.’’ Aperiodic long-...
متن کاملLyapunov Exponents
We are interested in iterates of the logistic map T : [0, 1] → [0, 1] defined by
متن کاملLyapunov exponents, dual Lyapunov exponents, and multifractal analysis.
It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of one-dimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps. (c) 1999 American Institute of Physics.
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2006
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/19/10/010