Related papers: Lyapunov exponents for binary substitutions of con…

We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schr\"odinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose…

The Lyapunov exponents of locally constant GL(2;C)-cocycles over Bernoulli shifts depend continuously on the cocycle and on the invariant probability. The Oseledets decomposition also depends continuously on the cocycle, in measure.

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.…

Critical eigenstates are usually identified through wave-function geometry in a chosen basis, such as participation ratios, multifractal spectra, or finite-size scaling. Here we formulate criticality instead as a dual-space Lyapunov…

This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…

We prove that for every discrete-time linear switching system in two complex variables and with finitely many switching states, either the system is Lyapunov stable or there exists a trajectory which escapes to infinity with at least linear…

In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…

This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…

We decide the stability and compute the Lyapunov exponent of continuous-time linear switching systems with a guaranteed dwell time. The main result asserts that the discretization method with step size~$h$ approximates the Lyapunov exponent…

We show the existence of nonautonomous invariant manifolds for planar, asymptotically autonomous differential equations, that have equilibrium solutions with zero Lyapunov spectrum. These invariant manifolds correspond to the stable and…

We prove that the Lyapunov exponents, cosidered as functions of measures with non compact support, are semicontinuous with respect to the Wasserstein topology but not with respect to the weak* topology. Moreover, we prove that they are not…

We collect some applications of the variational formula established by Schr\"oder (1988) and Rue\ss (2013) for the quenched Lyapunov exponent of Brownian motion in stationary and ergodic nonnegative potential. We show for example that the…

We consider a similar type of scenario for the disappearance of uniform of hyperbolicity as in Bjerkl\"ov and Saprykina (2008, Nonlinearity 21), where it was proved that the minimum distance between invariant stable and unstable bundles has…

We give lower and upper bounds on both the Lyapunov exponent and generalised Lyapunov exponents for the random product of positive and negative shear matrices. These types of random products arise in applications such as fluid stirring…

In this paper, we study rigidity problems between Lyapunov exponents along periodic orbits and geometric structures. More specifically, we prove that for a surface M without focal points, if the value of the Lyapunov exponents is constant…

Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…

We show that SL(2,R) cocycles with a positive Lyapunov exponent are dense in all regularity classes and for all non-periodic dynamical systems. For Schr\"odinger cocycles, we show prevalence of potentials for which the Lyapunov exponent is…

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…

In this note we study the multifractal spectrum of Lyapunov exponents for interval maps with infinitely many branches and a parabolic fixed point. It turns out that, in strong contrast with the hyperbolic case, the domain of the spectrum is…

For a strongly dissipative H\'enon-like map at the first bifurcation parameter at which the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set, we effect a multifractal analysis, i.e., decompose the set…