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Determining Lyapunov Exponents from a Time Series
 Physica
, 1985
"... We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of n ..."
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Cited by 495 (1 self)
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We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence
LYAPUNOV 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 ..."
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Cited by 3 (0 self)
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The analysis of potentially chaotic behavior in biological and biomedical phenomena has attracted great interest in recent years (1–6). Although no universally accepted
ON QUANTUM LYAPUNOV EXPONENTS
, 2005
"... Abstract. It was shown that quantum analysis constitutes the proper analytic basis for quantization of Lyapunov exponents in the Heisenberg picture. Differences among various quantizations of Lyapunov exponents are clarified. 1. ..."
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Abstract. It was shown that quantum analysis constitutes the proper analytic basis for quantization of Lyapunov exponents in the Heisenberg picture. Differences among various quantizations of Lyapunov exponents are clarified. 1.
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 onedimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps. © 1999 American Institute of ..."
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It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of onedimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps. © 1999 American Institute
Lyapunov Exponents of Free Operators
, 2008
"... Lyapunov exponents of a dynamical system are a useful tool to gauge the stability and complexity of the system. This paper offers a definition of Lyapunov exponents for a sequence of free linear operators. The definition is based on the concept of the extended FugledeKadison determinant. We establi ..."
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Cited by 3 (1 self)
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Lyapunov exponents of a dynamical system are a useful tool to gauge the stability and complexity of the system. This paper offers a definition of Lyapunov exponents for a sequence of free linear operators. The definition is based on the concept of the extended FugledeKadison determinant. We
Maximal Lyapunov exponent at crises
 Phys. Rev. E
, 1996
"... We study the variation of Lyapunov exponents of simple dynamical systems near attractorwidening and attractormerging crises. The largest Lyapunov exponent has universal behaviour, showing abrupt variation as a function of the control parameter as the system passes through the crisis point, either ..."
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Cited by 1 (0 self)
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We study the variation of Lyapunov exponents of simple dynamical systems near attractorwidening and attractormerging crises. The largest Lyapunov exponent has universal behaviour, showing abrupt variation as a function of the control parameter as the system passes through the crisis point, either
Lyapunov Exponents of Symmetric Attractors
, 2006
"... The Lyapunov exponents of symmetric attractors can be forced to be multiple by \instantaneous symmetries " which x the attractor pointwise. In this paper, we show that \symmetries on average " which x the attractor as a set may lead to further multiplicities. This work is motivated by, an ..."
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The Lyapunov exponents of symmetric attractors can be forced to be multiple by \instantaneous symmetries " which x the attractor pointwise. In this paper, we show that \symmetries on average " which x the attractor as a set may lead to further multiplicities. This work is motivated by
Recurrence, Dimensions And Lyapunov Exponents
, 2001
"... We show that the Poincaré return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times. ..."
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Cited by 12 (2 self)
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We show that the Poincaré return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times.
RECURRENCE AND LYAPUNOV EXPONENTS
, 2002
"... Abstract. We prove two inequalities between the Lyapunov exponents of a diffeomorphism and its local recurrence properties. We give examples showing that each of the inequalities is optimal. 1. ..."
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Cited by 6 (0 self)
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Abstract. We prove two inequalities between the Lyapunov exponents of a diffeomorphism and its local recurrence properties. We give examples showing that each of the inequalities is optimal. 1.
Upper Quantum Lyapunov Exponent and
, 2005
"... We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skewproduct systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in ..."
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We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skewproduct systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space
Results 1  10
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8,989