Lyapunov irregular set of Banach cocycles

Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Topological entropy (37B40) Symbolic dynamics (37B10) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)

Cites Work

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Generic property of irregular sets in systems satisfying the specification property
Cocycles with one exponent over partially hyperbolic systems
The sets of divergence points of self-similar measures are residual
Ergodic properties of systems with asymptotic average shadowing property
Nonexistence of Lyapunov exponents for matrix cocycles
Livšic theorem for matrix cocycles
Lyapunov exponents for products of matrices and multifractal analysis. II: General matrices
Continuity of subadditive pressure for self-affine sets
Topological pressure and the variational principle for noncompact sets
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Variational principles for topological entropies of subsets
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Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
Subadditive and multiplicative ergodic theorems
Quasi-multiplicativity of typical cocycles
Irregular sets are residual
Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
Simplicity of Lyapunov spectra: a sufficient criterion
Irregular sets, the $𝛽$-transformation and the almost specification property
RECURRENCE, DIMENSION AND ENTROPY
On the irregular points for systems with the shadowing property
The irregular set for maps with the specification property has full topological pressure
Invariant sets with zero measure and full Hausdorff dimension
On the variational principle for the topological entropy of certain non-compact sets
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Extremely non-normal numbers
Topological Entropy for Noncompact Sets
Lyapunov exponents with multiplicity 1 for deterministic products of matrices
Topological entropy for divergence points
Cohomology of fiber bunched cocycles over hyperbolic systems
Ergodic average of typical orbits and typical functions

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