Let λ i (A), i=1,···,n, (λ i (A)≤λ i+1 (A)), be the characteristic exponents of Lyapunov for (1). denotes the metric space consisting of the equations of the type (1), with the metric ρ(A,B)=sup t∈R + ∥B(t)-A(t)∥· Take arbitrarily x ˙=A(t)x and...
Perturbation theory for Lyapunov exponents of an Anderson model on a strip It is proven that the inverse localization length of an Anderson model on a strip of width L is bounded above by L /λ 2 for small values of the coupling... H Schulz-Baldes - 《Geometric & Functional Analysis ...
The main purpose of this paper is to stress the importance of Lyapunov exponents for the study of nonlinear deterministic and stochastic systems. After some introductory examples we present basic resudoi:10.1007/978-3-642-46508-6_2L. Arnold...
University Lecture Series(共35册),这套丛书还有 《Function Theory and lp Spaces》《Koszul Cohomology and Algebraic Geometry》《Lectures on Differential Galois Theory (University Lecture Series)》《Lectures on the Riemann Zeta function》《J-holomorphic Curves and Quantum Cohomology》等。 我来说两句 短评...
We discuss certain recent metric space methods and some of the possibilitiesthese methods provide, with special focus on various generalizations ofLyapunov exponents originally appearing in the theory of dynamical systems anddifferential equations. These generalizations appear for example in topology,group th...
A renormalization group analysis of the effects of noise is developed. We ... JV Kapustina,AP Kuznetsov,SP Kuznetsov,... - 《Physical Review E》 被引量: 3发表: 2001年 Discrete Rssler Oscillators: Maps and Their Ensembles As the main research tool we used the method of Lyapunov exponents ...
D Zhang,A Nagurney - 《Journal of Optimization Theory & Applications》 被引量: 93发表: 1997年 Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k) We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of CP(k) and prove...
The invariant manifold theory is a nonlinear counterpart of the linear theory of Lyapunov exponents. We first give a rough description of this theory. Corresponding to each negative Lyapunov exponent λ(i)(ω, x) < 0 at a typical point (ω, x), one can consider the collection of points ...
we indicate the chaotic behaviors of the system by means of Lyapunov exponents, bifurcation diagrams versus all parameters along the state variables, phase portraits and time histories with different trajectories and initial conditions. The necessary conditions to eliminate the chaotic vibration of the sy...
● Master Mathematical Tools: Become proficient in techniques like phase space analysis, Poincaré sections, Lyapunov exponents, and fractal dimension calculation. ○ "An Exploration of Chaos" by Argyris, Faust, and Haase and "Chaos, Fractals, and Noise" by Lasota and Mackey offer guidance on thes...