The generalised Berger-Wang formula and the spectral radius of linear cocycles

DOI10.1016/j.jfa.2011.09.021zbMath1254.47006arXiv0906.2915OpenAlexW2962978872MaRDI QIDQ665508

Ian D. Morris

Publication date: 5 March 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.2915

zbMATH Keywords

spectral radiusmeasure of noncompactnessjoint spectral radiusessential spectral radiusmultiplicative ergodic theoremlinear cocycleBerger-Wang formula

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Measures of noncompactness and condensing mappings, (K)-set contractions, etc. (47H08)

Related Items (16)

Ergodic properties of matrix equilibrium states ⋮ Continuity of spectral radius over hyperbolic systems ⋮ Topological radicals and joint spectral radius ⋮ Bounds on the joint and generalized spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators ⋮ Boundedness, compactness, and invariant norms for Banach cocycles over hyperbolic systems ⋮ Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equations ⋮ Inequalities and equalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators ⋮ Characterization of dominated splittings for operator cocycles acting on Banach spaces ⋮ Periodic approximation of Lyapunov exponents for Banach cocycles ⋮ The Berger-Wang formula for the Markovian joint spectral radius ⋮ Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles ⋮ Totally ergodic generalised matrix equilibrium states have the Bernoulli property ⋮ On the spectral radius of compact operator cocycles ⋮ A new inequality about matrix products and a Berger-Wang formula ⋮ Ergodic optimization in dynamical systems ⋮ Inequalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Livšic theorem for matrix cocycles
• Asymptotic stability and generalized Gelfand spectral radius formula
• Fibres dynamiques asymptotiquement compacts, exposants de Lyapunov. Entropie. Dimension. (Asymptotically compact dynamical bundles, Lyapunov exponents. Entropy. Dimension)
• Lyapunov indicator of discrete inclusions. I
• Characteristic exponents and invariant manifolds in Hilbert space
• Algebraic unsolvability of problem of absolute stability of desynchronized systems
• Sets of matrices all infinite products of which converge
• Bounded semigroups of matrices
• Manifolds, tensor analysis, and applications.
• On growth rates of subadditive functions for semiflows
• Volterra semigroups have invariant subspaces
• Joint spectral radius, operator semigroups, and a problem of W. Wojtyński
• A formula with some applications to the theory of Lyapunov exponents
• Stability of discrete linear inclusion
• Lyapunov and dynamical spectra for Banach state-spaces
• Semigroups of operators and measures of noncompactness
• Formulae for joint spectral radii of sets of operators
• Coherent structures and isolated spectrum for Perron–Frobenius cocycles
• Random Matrices and Their Applications
• Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
• On codes that avoid specified differences
• Semi-uniform ergodic theorems and applications to forced systems
• Formulas for the Joint Spectral Radius of Non-Commuting Banach Algebra Elements
• The radius of the essential spectrum
• On the zero-stability of variable stepsize multistep methods: The spectral radius approach

This page was built for publication: The generalised Berger-Wang formula and the spectral radius of linear cocycles