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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 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
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
The variational principle for products of nonnegative
, 2003
"... Let (A, σ) be a subshift of finite type and let M(x) be a continuous function on A taking values in the set of nonnegative matrices. We set up the variational principle between the pressure function, entropy and Lyapunov exponent for M on A. We also present some properties of equilibrium states. Ma ..."
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Let (A, σ) be a subshift of finite type and let M(x) be a continuous function on A taking values in the set of nonnegative matrices. We set up the variational principle between the pressure function, entropy and Lyapunov exponent for M on A. We also present some properties of equilibrium states
Dynamics of rational maps: Lyapunov exponents, bifurcations
 Math. Ann
, 2003
"... Abstract. Let L(f) = � log �Df � dµf denote the Lyapunov exponent of a rational map, f: P 1 → P 1. In this paper, we show that for any holomorphic family of rational maps {fλ: λ ∈ X} of degree d> 1, T (f) = dd c L(fλ) defines a natural, positive (1,1)current on X supported exactly on the bifu ..."
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Cited by 38 (3 self)
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and pseudoconvex sets K ⊂ C 2 and show that the Levi measure (determined by the geometry of ∂K) is the unique equilibrium measure. Such K ⊂ C 2 correspond to metrics of nonnegative curvature on P 1, and we obtain a variational characterization of curvature.
Numerical solution of the stable, nonnegative definite Lyapunov equation
 IMA J. Numer. Anal
, 1982
"... We discuss the numerical solution of the Lyapunov equation ..."
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Cited by 112 (2 self)
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We discuss the numerical solution of the Lyapunov equation
Lyapunov exponents: How frequently are dynamical systems hyperbolic?
 IN ADVANCES IN DYNAMICAL SYSTEMS. CAMBRIDGE UNIV
, 2004
"... Lyapunov exponents measure the asymptotic behavior of tangent vectors under iteration, positive exponents corresponding to exponential growth and negative exponents corresponding to exponential decay of the norm. Assuming hyperbolicity, that is, that no Lyapunov exponents are zero, Pesin theory p ..."
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Cited by 32 (2 self)
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Lyapunov exponents measure the asymptotic behavior of tangent vectors under iteration, positive exponents corresponding to exponential growth and negative exponents corresponding to exponential decay of the norm. Assuming hyperbolicity, that is, that no Lyapunov exponents are zero, Pesin theory
Results 1  10
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2,295