Geodesic
An example of a linear discrete system with unstable Lyapunov exponents
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 2, pp. 169-176 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a discrete time-varying linear system \begin{equation} x(m+1)=A(m)x(m),\quad m\in\mathbb Z,\quad x\in\mathbb R^n, \tag{1} \end{equation} where $A(\cdot)$ is completely bounded on $\mathbb N$, i.e., $\sup_{m\in\mathbb N}\bigl(\|A(m)\|+\|A^{-1}(m)\|\bigr)<\infty$. Let $\lambda_1(A)\le\ldots\le\lambda_n(A)$ be the Lyapunov spectrum of the system (1). It is called stable if for any $\varepsilon>0$ there exists a $\delta>0$ such that for every completely bounded $n\times n$-matrix $R(\cdot)$, $\sup_{m\in\mathbb N}\|R(m)-E\|<\delta$, the inequality $$\max_{j=1,\ldots,n}|\lambda_j(A)-\lambda_j(AR)|<\varepsilon $$ holds. We construct an example of the system (1) with unstable Lyapunov spectrum.
Keywords: discrete time-varying linear system, Lyapunov exponents
Mots-clés : perturbations of coefficients. 
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I. N. Banshchikova. An example of a linear discrete system with unstable Lyapunov exponents. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 2, pp. 169-176. http://geodesic.mathdoc.fr/item/VUU_2016_26_2_a2/

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