Perturbation theory for the approximation of stability spectra by QR methods for sequences of linear operators on a Hilbert space

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• 作者：M. Badawy ; ^{mbadawy@math.ku.edu} ; E. Van Vleck ^{evanvleck@math.ku.edu}
• 关键词：Lyapunov exponents ; Sacker&ndash ; Sell spectrum ; Dynamical spectrum ; Stability spectra ; Exponential dichotomy ; Integral separation ; Newton&ndash ; Kantorovich theorem ; Sequences of operators ; QR factorization ; QR technique ; Skew product semiflow ; Infinite di
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 July, 2012
• 卷：437
• 期：1
• 页码：37-59
• 文件大小：406 K

摘要

In this paper, we develop a perturbation analysis for stability spectra (Lyapunov exponents and Sacker-Sell spectrum) for products of operators on a Hilbert space (both real and complex) based upon the discrete QR technique. Error bounds are obtained in both the integrally separated and non-integrally separated cases that correspond to distinct and multiple eigenvalues, respectively, for a single linear operator. We illustrate our results using a linear parabolic partial differential equation in which the strength of the integral separation (the time varying analogue of gaps between eigenvalues) determines the sensitivity of the stability spectra to perturbation.