相关论文: Lyapunov exponents from unstable periodic orbits i…

We establish that the entropy production rate of a classically chaotic Hamiltonian system coupled to the environment settles, after a transient, to a meta-stable value given by the sum of positive generalized Lyapunov exponents. A…

This report investigates the dynamical stability conjectures of Palis and Smale, and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical…

We present a heuristic derivation of the maximal Lyapunov exponent $\gamma$ of homogeneous turbulence which yields two new relations, a sweeping relation and the scaling of the uncertainty field's integral length $L_{\Delta}$. These…

We use finite-time Lyapunov exponent (FTLE) distributions to probe transition mechanisms in high-dimensional reservoir maps trained on low-dimensional chaotic dynamics across multiple regimes. While trained reservoirs accurately predict…

The Lyapunov spectrum describes the exponential growth, or decay, of infinitesimal phase-space perturbations. The perturbation associated with the maximum Lyapunov exponent is strongly localized in space, and only a small fraction of all…

The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…

Chaotic flow is studied in a series of numerical magnetohydrodynamical simulations that use the shearing box formalism. This mimics important features of local accretion disk dynamics. The magnetorotational instability gives rise to flow…

Dynamical control of excitable biological systems is often complicated by the difficult and unreliable task of pre-control identification of unstable periodic orbits (UPOs). Here we show that, for both chaotic and nonchaotic systems, UPOs…

An investigation of the distribution of finite time trajectory divergence is performed on an Atmospheric Global Circulation Model. The distribution of the largest local Lyapunov exponent shows a significant probability for negative values…

A new diffusion mechanism from the neighborhood of elliptic equilibria for Hamiltonian flows in three or more degrees of freedom is introduced. We thus obtain explicit real entire Hamiltonians on $\R^{2d}$, $d\geq 4$, that have a Lyapunov…

Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of spatio-temporal chaos and turbulence. Finding these UPOs is however notoriously difficult. Matrix-free loop convergence algorithms deform entire…

We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

We obtain a local stable manifold theorem for perturbations of nonautonomous linear difference equations possessing a very general type of nonuniform dichotomy, possibly with different growth rates in the uniform and nonuniform parts. We…

Stable chaos refers to the long irregular transients, with a negative largest Lyapunov exponent, which is usually observed in certain high-dimensional dynamical systems. The mechanism underlying this phenomenon has not been well studied so…

Recent work on many particle system reveals the existence of regular collective perturbations corresponding to the smallest positive Lyapunov exponents (LEs), called hydrodynamic Lyapunov modes. Until now, however, these modes are only…

We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models; depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first…

In this Letter we show that the analysis of Lyapunov-exponents fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a Gaussian approximation for the large deviation function that…

This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port--Hamiltonian systems including second order models such as the Euler--Bernoulli beam. The control design is achieved using…

We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of…