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On the Sum of the NonNegative Lyapunov Exponents for Some Cocycles Related to the Anderson Model
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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 462 (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
, 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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Cited by 1 (0 self)
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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
Nonlinear Processes in Geophysics On the Kalman Filter error covariance collapse
"... Abstract. When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N++N0 where N+ and N0 are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstabl ..."
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into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with nonnegative Lyapunov exponents. Theoretical arguments and numerical
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"... This work concerns the study of the asymptotics of their random products which is characterized by the Lyapunov exponents. One way [BL, CL] to define these exponents is to use a formalism of second quantization. For p = 1,..., L, let ΛpC2L denote the Hilbert space of the antisymmetrized pfold tens ..."
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fold tensor products of C2L, the scalar product being given via the determinant. Given a linear map T on C2L, its second quantized ΛpT on ΛpC2L is defined as usual. Now the whole family of nonnegative Lyapunov exponents γ1 ≥ γ2 ≥... ≥ γL ≥ 0 are defined by: p∑ l=1 γl = lim
Cellular automata and Lyapunov exponents
 Nonlinearity
"... The first definition of Lyapunov exponents (depending on a probability measure) for a onedimensional cellular automaton were introduced by Shereshevsky in 1991. The existence of an almost everywhere constant value for each of the two exponents (left and right), requires particular conditions for th ..."
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Cited by 7 (2 self)
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The first definition of Lyapunov exponents (depending on a probability measure) for a onedimensional cellular automaton were introduced by Shereshevsky in 1991. The existence of an almost everywhere constant value for each of the two exponents (left and right), requires particular conditions
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.
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
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
Results 1  10
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141,061