相关论文: Recurrence and lyapunov exponents

We prove that the Lyapunov exponents of random products in a (real or complex) matrix group depends continuously on the matrix coefficients and probability weights. More generally, the Lyapunov exponents of the random product defined by any…

We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.

We discuss several numerical methods for calculating Lyapunov exponents (a quantitative measure of chaos) in systems of ordinary differential equations. We pay particular attention to constrained systems, and we introduce a variety of…

For quasi-linear elliptic equations we detect relevant properties which remain invariant under the action of a suitable class of diffeomorphisms. This yields a connection between existence theories for equations with degenerate and…

We study maps on the torus $\mathbb{T}^2$ that are of the form $F(x,y) = (bx, f_x(y))$, where $b\geq 2$ is an integer. We establish an open class of $C^1$-maps, with $f_x(y)$ that are typically non-monotonic in $x$, for which the Lyapunov…

In this paper, two types of Lyapunov exponents: random Lyapunov exponents and directional Lyapunov exponents, and the corresponding entropies: random entropy and directional entropy, are considered for smooth $\mathbb{Z}^k$-actions. The…

In this note we discuss three interconnected problems about dynamics of Hamiltonian or, more generally, just smooth diffeomorphisms. The first two concern the existence and properties of the maps whose iterations approximate the identity…

We show the finiteness of homoclinic classes carrying measures with large Lyapunov exponents for $\mathcal{C}^2$ surface diffeomorphisms. As a consequence, we derive the finiteness of the set of ergodic measures of maximal entropy, in the…

In this paper we present a new approach to prove effective results in Diophantine approximation. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with…

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 consider a boundary value problem involving conformable derivative of order $\alpha ,$ $1<\alpha <2$ and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's…

We study proximal random dynamical systems of homeomorphisms of the circle without a common fixed point. We prove the existence of two random points that govern the behavior of the forward and backward orbits of the system. Assuming the…

We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are…

We prove that periodic asymptotic expansiveness introduced in \cite{em} implies the equidistribution of periodic points to measures of maximal entropy. Then following Yomdin's approach \cite{Yom} we show by using semi-algebraic tools that…

The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincar{\'e} inequality, the existence of some Lyapunov function and the exponential…

We prove that infinitely renormalizable contracting Lorenz maps with bounded geometry or the so-called {\it a priori bounds} satisfies the slow recurrence condition to the singular point $c$ at its two critical values $c_1^-$ and $c_1^+$.…

A new approach is used to describe the large time behavior of the non-local differential equation initially studied in [3]. Our approach is based upon the existence of infinitely many Lyapunov functionals and allows us to extend the…

Reactivity, contractivity, and Lyapunov exponents are powerful tools for studying the stability properties of dynamical systems and have been extensively investigated in the literature for decades. In this paper, we review and extend the…

We exhibit an example of discontinuity point for the Lyapunov exponents as a function of the cocycle in the $\alpha$-H\"older topology. The linear cocycle taking values in $SL(2, \mathbb{R})$ is locally constant and defined over a Bernoulli…

In this paper, a necessary and sufficient condition for the stability of Lyapunov exponents of linear differential system are proved in the sense that the equations satisfy the weaker form of integral separation instead of its classical…