相关论文: Quasi-multiplicativity of typical cocycles

We develop a higher-dimensional extension of multifractal analysis for typical fiber-bunched linear cocycles. Our main result is a relative variational principle, which shows that the topological entropy of Lyapunov exponent level sets can…

We prove that generic fiber-bunched and H\"older continuous linear cocycles over a non-uniformly hyperbolic system endowed with a u-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by…

We prove that Lyapunov exponents of typical H\"older continuous fiber bunched linear cocycles over singular hyperbolic flows have multiplicity 1: the subspace of exceptional cocycles has infinite codimension.

An analytic quasi-periodic cocycle is a linear cocycle over a fixed ergodic torus translation of one or several variables, where the fiber action depends analytically on the base point. Consider the space of all such cocycles of any given…

We prove that the Lyapunov exponents of typical fiber bunched linear cocycles over Lorenz-like flows have multiplicity one: the set of exceptional cocycles has infinite codimention, i.e. it is locally contained in finite unions of closed…

In this paper, we study the multifractal formalism of Lyapunov exponents for typical cocycles. We establish a variational relation between the Legendre transform of topological pressure of the generalized singular value function and…

In this paper, we show that a locally constant cocycle $\mathcal{A}$ is $k$-quasi multiplicative under the irreducibility assumption. More precisely, we show that if $\mathcal{A}^t$ and $\mathcal{A}^{\wedge m}$ are irreducible for every $t…

We consider H\"older continuous $GL(d,\mathbb R)$-valued cocycles, and more generally linear cocycles, over an accessible volume-preserving center-bunched partially hyperbolic diffeomorphism. We study the regularity of a conjugacy between…

Avila and Viana exhibit an explicit sufficient condition for the Lyapunov exponents of a linear cocycle over a Markov map to have multiplicity 1. Here, in terms of geometric perturbations, we prove that this sufficient criterion is generic…

We provide conditions which imply the continuity of the Lyapunov exponents for non-uniformly fiber-bunched cocycles in $SL(2,\mathbb{R})$. The main theorem is an extension of the result of Backes, Brown and Butler and gives a partial answer…

We give examples of locally constant $SL(2,\mathbb{R})$-cocycles over a Bernoulli shift which are discontinuity points for Lyapunov exponents in the H\"older topology and are arbitrarily close to satisfying the fiber bunching inequality.…

We prove a new characterization of uniform hyperbolicity for fiber-bunched cocycles. Specifically, we show that the existence of a uniform gap between the Lyapunov exponents of a fiber-bunched $SL(2,\mathbb{R})$-cocycle defined over a…

We study ergodic optimization and multifractal behavior of Lyapunov exponents for matrix cocycles. We show the continuity of the entropy spectrum at the boundary of Lyapunov spectrum in the sense that $h_{top}(E(\alpha_{t}))\ \rightarrow…

This paper develops a quantitative regularity theory for the Lyapunov exponents of random products of matrices in $\operatorname{GL}(2,\mathbb{R})$, with extensions to $\operatorname{GL}(d,\mathbb{R})$ for all $d \geq 2$. At every compactly…

We derive large deviations type (LDT) estimates for linear cocycles over an ergodic multifrequency torus translation. These models are called quasi-periodic cocycles. We make the following assumptions on the model: the translation vector…

We prove a conjecture of Viana which states that Lyapunov exponents vary continuously when restricted to $GL(2,\mathbb{R})$-valued cocycles over a subshift of finite type which admit invariant holonomies that depend continuously on the…

We establish some conditions under which $\text{GL}(d,\mathbb{R})$-valued cocycles over a subshift of finite type, equipped with an equilibrium state, exhibit exponential asymptotics for the spectral radius. Specifically, we show that the…

We show the sum of the first $k$ Lyapunov exponents of linear cocycles is an upper semicontinuous function in the $L^p$ topologies, for any $1 \le p \le \infty$ and $k$. This fact, together with a result from Arnold and Cong, implies that…

In this paper, we study the size of the level sets of all Lyapunov exponents. For typical cocycles, we establish a variational relation between the topological entropy of the level sets of Lyapunov exponents and the topological pressure of…

We show that on a dense open set of analytic one-frequency complex valued cocycles in arbitrary dimension Oseledets filtration is either dominated or trivial. The underlying mechanism is different from that of the Bochi-Viana Theorem for…