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16,551
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
Lyapunov Exponents
, 2008
"... It is proven that for a C 1generic symplectic diffeomorphism f of any closed manifold, the Oseledets splitting along almost every orbit is either trivial or partially hyperbolic. In addition, if f is not Anosov then all the exponents in the center bundle vanish. This establishes in full a result an ..."
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It is proven that for a C 1generic symplectic diffeomorphism f of any closed manifold, the Oseledets splitting along almost every orbit is either trivial or partially hyperbolic. In addition, if f is not Anosov then all the exponents in the center bundle vanish. This establishes in full a result
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 456 (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
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 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
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.
On the notion of quantum Lyapunov exponent.
, 2005
"... Abstract. Classical chaos refers to the property of trajectories to diverge exponentially as time t → ∞. It is characterized by a positive Lyapunov exponent. There are many different descriptions of quantum chaos. The one related to the notion of generalized (quantum) Lyapunov exponent is based eith ..."
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Abstract. Classical chaos refers to the property of trajectories to diverge exponentially as time t → ∞. It is characterized by a positive Lyapunov exponent. There are many different descriptions of quantum chaos. The one related to the notion of generalized (quantum) Lyapunov exponent is based
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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16,551