Related papers: Lyapunov exponents and bifurcation current for pol…

We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so called continuous type, where the rate of expansion of perturbations is obtained for all times,…

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 introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of CP(k) and prove that it is equivalent to the stability of repelling cycles and equivalent to the existence of some measurable…

Starting from a hyperbolic toral automorphism, we obtain, for a small volume preserving perturbation, an exact and rigorous second order perturbation expansion of the Lyapunov exponents.

An algorithm is presented here, for discovering Hopf-Bifurcation varieties of polynomial dynamical systems. It is based on the expression of specific polynomials, as sums of products of first degree polynomials, with parametrical…

This is the first article in a series that aims at classifying partial sections of flows, that is a general family of transverse surfaces. In this part, we deal with the dynamical aspect of the question. Given a flow on a compact manifold…

We consider the set of partially hyperbolic symplectic diffeomorphisms which are accessible, have 2-dimensional center bundle and satisfy some pinching and bunching conditions. In this set, we prove that the non-uniformly hyperbolic maps…

We consider a generalisation of Ulam's method for approximating invariant densities of one-dimensional chaotic maps. Rather than use piecewise constant polynomials to approximate the density, we use polynomials of degree n which are defined…

A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the…

We establish (i) stability of Lyapunov exponents and (ii) convergence in probability of Oseledets spaces for semi-invertible matrix cocycles, subjected to small random perturbations. The first part extends results of Ledrappier and Young to…

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…

In this paper we prove the continuity of all Lyapunov exponents, as well as the continuity of the Oseledets decomposition, for a class of irreducible cocycles over strongly mixing Markov shifts. Moreover, gaps in the Lyapunov spectrum lead…

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…

We characterize geometrically the Lyapunov exponents of a cocycle (of arbitrary rank) with respect to a harmonic current defined on a hyperbolic Riemann surface lamination. Our characterizations are formulated in terms of the expansion…

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…

We study the regularity of Lyapunov exponents as functions on the space of compactly supported probability measures on $\mathrm{GL}(d,\mathbb{R})$. We prove that the Lyapunov exponents are pointwise log-H\"older continuous with respect to…

We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with…

In this paper we review the use of techniques of positive currents for the study of parameter spaces of one-dimensional holomorphic dynamical systems (rational mappings on P^1 or subgroups of the Moebius group PSL(2,C)). The topics covered…

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…

This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic…