Related papers: Singular analytic linear cocycles with negative in…
We consider linear cocycles over non-uniformly hyperbolic dynamical systems. The base system is a diffeomorphism $f$ of a compact manifold $X$ preserving a hyperbolic ergodic probability measure $\mu$. The cocycle $A$ over $f$ is Holder…
In 2019 Anthony Quas, Philippe Thieullen and Mohamed Zarrabi introduced the concept of strong fast invertibility for linear cocycles. It relates the growth of volumes between different initial times and, together with a condition on…
We study the regularity of Lyapunov exponents for random linear cocycles taking values in $\Mat_m(\R)$ and driven by i.i.d. processes. Under three natural conditions - finite exponential moments, a spectral gap between the top two Lyapunov…
We consider symplectic cocycles over two classes of partially hyperbolic diffeomorphisms: having compact center leaves and time one maps of Anosov flows. We prove that the Lyapunov exponents are non-zero in an open and dense set in the…
In the present paper we give a positive answer to some questions posed by Viana on the existence of positive Lyapunov exponents for Hamiltonian linear differential systems. We prove that there exists an open and dense set of Hamiltonian…
From the analyticity properties of the equation governing infinitesimal perturbations, it is shown that all stability properties of spatially extended 1D systems can be derived from a single function that we call entropy potential since it…
In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic…
After relating the notion of $\omega$-recurrence in skew products to the range of values taken by partial ergodic sums and Lyapunov exponents, ergodic $\mathbb{Z}$-valued cocycles over an irrational rotation are presented in detail. First,…
Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove the analogous results for finite-dimensional Malcev, Jordan,…
We provide an explicit lower bound for the the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model. In particular, for the Anderson model on a strip of width $ W $ the lower bound is proportional to $…
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…
For analytic quasi-periodic Schr\"odinger cocycles, You and Zhang [9] proved that the Lyapunov exponent is H\"older continuous for weak Liouville frequency. In this paper, we prove that the H\"older continuity also holds if the analytic…
We study lower bounds on the Lyapunov exponent associated with one-frequency quasiperiodic Schr\"odinger operators with an added finite valued background potential. We prove that, for sufficiently large coupling constant, the Lyapunov…
In this paper, we first prove the strong Birkhoff Ergodic Theorem for subharmonic functions with the irrational shift on the Torus. Then, it is applied to the analytic quasi-periodic Jacobi cocycles. We show that if the Lyapunov exponent of…
We study regularity properties of the Lyapunov exponent L of quasiperiodic operators with analytic potential, under no assumptions on the Diophantine class of the frequency. We prove that L is jointly continuous, in frequency and energy, at…
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…
We study Schrodinger operators with a one-frequency analytic potential, focusing on the transition between the two distinct local regimes characteristic respectively of large and small potentials. From the dynamical point of view, the…
We prove the positivity of the top Lyapunov exponent of the twisted (spectral) cocycle, associated with IETs, with respect to a family of natural invariant measures. The proof relies on relating the top exponent to limits of exponents along…
It follows from Oseledec Multiplicative Ergodic Theorem that the Lyapunov-irregular set of points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In…
Given a finite set of quasi-periodic cocycles the random product of them is defined as the random composition according to some probability measure. We prove that the set of $C^r$, $0\leq r \leq \infty$ (or analytic) $k+1$-tuples of quasi…