منابع مشابه
Lyapunov 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.
متن کاملLyapunov 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
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A smooth distribution, invariant under a dynamical system, integrates to give an invariant foliation, unless certain resonance conditions are present.
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We prove two inequalities between the Lyapunov exponents of a diffeomorphism and some characteristics of its local recurrence properties. We give examples of linear hyperbolic maps of the torus showing that each of the inequalities is optimal. 2000 Math. Subj. Class. Primary: 37B20; Secondary: 37C45.
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 1987
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/917027