Perturbation theory for the approximation of stability spectra by QR methods for sequences of linear operators on a Hilbert space
Copyright policy )Perturbation theory for the approximation of stability spectra by QR methods for sequences of linear operators on a Hilbert space
The authors develop a quantitative perturbation theory for the approximation of stability spectra of sequences of infinite dimensional operators based on an infinite dimensional \(QR\) technique for determining Lyapunov exponents and Sacker-Sell spectrum. The results apply also in the case of stable but not necessarily distinct Lyapunov exponents. The perturbation bounds are obtained by posing an appropriate zero finding problem and applying the Newton-Kantorovich theorem. As an illustration, the results are applied to a one-dimensional parabolic initial-boundary problem. The results are rather technical.
- University of Kansas United States
Stability of solutions, Dichotomy, trichotomy of solutions to ordinary differential equations, Perturbation theory of linear operators, Integral separation, QR technique, Skew product semiflow, Perturbation theory, dynamical system, integral separation, skew product flow, Newton–Kantorovich theorem, Discrete Mathematics and Combinatorics, Characteristic and Lyapunov exponents of ordinary differential equations, Spectrum, resolvent, Numerical Analysis, Algebra and Number Theory, Applications of operator theory to differential and integral equations, Hilbert space, Lyapunov exponents, QR factorization, Sacker–Sell spectrum, exponential dichotomy, Exponential dichotomy, Sequences of operators, Applications of operator theory in numerical analysis, perturbation of dynamical system, Stability of Lyapunov exponents, Infinite dimensional dynamical systems, Stability spectra, Sacker-Sell spectrum, Dynamical spectrum, Geometry and Topology, stability of Lyapunov exponents, Stability in context of PDEs, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Stability of solutions, Dichotomy, trichotomy of solutions to ordinary differential equations, Perturbation theory of linear operators, Integral separation, QR technique, Skew product semiflow, Perturbation theory, dynamical system, integral separation, skew product flow, Newton–Kantorovich theorem, Discrete Mathematics and Combinatorics, Characteristic and Lyapunov exponents of ordinary differential equations, Spectrum, resolvent, Numerical Analysis, Algebra and Number Theory, Applications of operator theory to differential and integral equations, Hilbert space, Lyapunov exponents, QR factorization, Sacker–Sell spectrum, exponential dichotomy, Exponential dichotomy, Sequences of operators, Applications of operator theory in numerical analysis, perturbation of dynamical system, Stability of Lyapunov exponents, Infinite dimensional dynamical systems, Stability spectra, Sacker-Sell spectrum, Dynamical spectrum, Geometry and Topology, stability of Lyapunov exponents, Stability in context of PDEs, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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