An improved estimate for the highest Lyapunov exponent in the method of freezing期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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An improved estimate for the highest Lyapunov exponent in the method of freezing

Authors:	G I Eleutheriadis

Institution:	Ektenepol, 14/3, 67100, Xanthi, Greece

Abstract:	Let $\dot x=A(t)x$ and $\lambda _k(t)$ be the eigenvalues of the matrix . The main result of the Method of Freezing states that if $\sup _J \\|A(t)\\|\leq M$ , $\sup _J\mathrm {max}_{1\leq k\leq n}\mathrm {Re}\,\lambda _k(t)\leq \rho$ and $\sup _J(\\|A(t)-A(s)\\|/\|t-s\|)\leq \delta$ , then $\begin{displaymath}x_\mathrm {max}\leq\rho +2M\lambda _\delta ,\end{displaymath}$ for the highest exponent $x_{\mathrm {max}}$ of the system, where $\begin{displaymath}\lambda _\delta =\left (\frac {C_n\delta }{4M^2}\right )^{\frac {1}{n+1}}.\end{displaymath}$ The previous best known value $C_n=\frac {n(n+1)}{2}$ and the substantially smaller values of are reduced to the still smaller value.

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