Extremal norms for fiber-bunched cocycles

DOI10.5802/jep.109zbMath1441.37059arXiv1808.02804OpenAlexW2980544769MaRDI QIDQ2328786

Jairo Bochi, Eduardo Garibaldi

Publication date: 16 October 2019

Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.02804

zbMATH Keywords

joint spectral radiusLyapunov exponentextremal normergodic optimizationlinear cocycle

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (11)

Livšic theorems for Banach cocycles: existence and regularity ⋮ Lyapunov spectrum properties and continuity of the lower joint spectral radius ⋮ Eigenvalue gaps for hyperbolic groups and semigroups ⋮ The Barabanov Norm is Generically Unique, Simple, and Easily Computed ⋮ Uniformity of singular value exponents for typical cocycles ⋮ A note on the marginal instability rates of two-dimensional linear cocycles ⋮ Construction and applications of proximal maps for typical cocycles ⋮ Bernoulli property of subadditive equilibrium states ⋮ Zero temperature limits of equilibrium states for subadditive potentials and approximation of maximal Lyapunov exponent ⋮ Thermodynamic formalism of \(\mathrm{GL}_2(\mathbb{R})\)-cocycles with canonical holonomies ⋮ The joint spectrum

Cites Work

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• Stability of discrete-time switching systems with constrained switching sequences
• The entropy of Lyapunov-optimizing measures of some matrix cocycles
• Ground states are generically a periodic orbit
• Cocycles with one exponent over partially hyperbolic systems
• Hölder foliations, revisited
• The Mañé-Conze-Guivarc'h lemma for amphidynamical systems
• A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory
• Livšic theorem for matrix cocycles
• Hölder foliations
• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• Some characterizations of domination
• Action minimizing invariant measures for positive definite Lagrangian systems
• An explicit Lipschitz constant for the joint spectral radius
• Extremal Lyapunov exponents: an invariance principle and applications
• Ergodic theorems. With a supplement by Antoine Brunel
• Lyapunov indicator of discrete inclusions. I
• Bounded semigroups of matrices
• The generalized spectral radius and extremal norms
• Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices. (Genericity of non-zero Lyapunov exponents for deterministic products of matrices)
• The boundedness of all products of a pair of matrices is undecidable
• Cohomology classes of dynamically non-negative \(C^ k\) functions.
• Linear switched dynamical systems on graphs
• Lectures on partial hyperbolicity and stable ergodicity
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• On bounded cocycles of isometries over minimal dynamics
• Cohomological inequalities for finite topological Markov chains
• Anosov representations and dominated splittings
• On the joint spectral radius for isometries of non-positively curved spaces and uniform growth
• A new inequality about matrix products and a Berger-Wang formula
• Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
• Simplicity of Lyapunov spectra: a sufficient criterion
• Ergodic optimization
• La condition de Walters
• Lyapunov minimizing measures for expanding maps of the circle
• Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture
• Aubry set for asymptotically sub-additive potentials
• SMOOTHNESS OF HOLONOMIES FOR CODIMENSION 1 HYPERBOLIC DYNAMICS
• A uniform dichotomy for generic ${\rm SL}(2,{\mathbb{R}})$ cocycles over a minimal base
• Rate of approximation of minimizing measures
• On minimal centers of attraction and generic points.
• On Arbitrary Sequences of Isomorphisms in R m →R m
• Continuity properties of the lower spectral radius
• Ergodic optimization in dynamical systems
• Lyapunov exponents with multiplicity 1 for deterministic products of matrices
• A sufficient condition for the subordination principle in ergodic optimization
• Mather sets for sequences of matrices and applications to the study of joint spectral radii
• Ergodic Optimization in the Expanding Case
• Adapted metrics for dominated splittings
• Unitarily Invariant Metrics on the Grassmann Space
• Differentiable dynamical systems
• Periodic Points and Measures for Axiom a Diffeomorphisms
• The dynamics of control. With an appendix by Lars Grüne
• Invariant manifolds
• Shadowing properties of \({\mathcal L}\)-hyperbolic homeomorphisms

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