相关论文: Accurate bounds on Lyapunov exponents for expandin…
A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in…
We revisit the numerical calculation of generalized Lyapunov exponents, $L$($q$), in deterministic dynamical systems. The standard method consists of adding noise to the dynamics in order to use importance sampling algorithms. Then $L$($q$)…
This paper is devoted to the study of $L_p$ Lyapunov-type inequalities for linear systems of equations with Neumann boundary conditions and for any constant $p \geq 1$. We consider ordinary and elliptic problems. The results obtained in the…
We give a construction of measures with partial sum of Lyapunov exponents bounded by below.
In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…
The spectrum of Lyapunov exponents is powerful tool for the analysis of the complex system dynamics. In the general framework of nonlinear dynamical systems a number of the numerical technics have been developed to obtain the spectrum of…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
The paper is concerned with the development of Lyapunov methods for the analysis of equilibrium stability in a dynamical system on the space of probability measures driven by a non-local continuity equation. We derive sufficient conditions…
In this paper we use a path-integral approach to represent the Lyapunov exponents of both deterministic and stochastic dynamical systems. In both cases the relevant correlation functions are obtained from a (one-dimensional) supersymmetric…
The Lyapunov spectra of random U(1) extensions of expanding maps on the torus were investigated in our previous work [NW2015]. Using the result, we extend the recent spectral approach for quenched limit theorems for expanding maps…
The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the existence of complete Lyapunov functions for semiflows…
We establish explicit exponential convergence estimates for the renewal theorem, in terms of a uniform component of the inter arrival distribution, of its Laplace transform which is assumed finite on a positive interval, and of the Laplace…
We prove that in an open and dense set, Symplectic linear cocycles over time one maps of Anosov flows, have positive Lyapunov exponents for SRB measures.
We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate…
We analyze the two-point motions of iterated function systems on the unit interval generated by expanding and contracting affine maps, where the expansion and contraction rates are determined by a pair $(M,N)$ of integers. This dynamics…
We propose a two-phase systematical framework for approximation algorithm design and analysis via Lyapunov function. The first phase consists of using Lyapunov function as an input and outputs a continuous-time approximation algorithm with…
We prove $l^p$-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of $p$ in all dimensions $n\ge 2$.
A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces. The classical function spaces for this purpose are H\"older spaces and Sobolev…
If E is a flat bundle of rank r over a K\"ahler manifold X, we define the Lyapunov spectrum of E: a set of r numbers controlling the growth of flat sections of E, along Brownian trajectories. We show how to compute these numbers, by using…
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…