相关论文: Lyapunov exponents and Hodge theory
We describe a method of writing down interacting equations for all the modes of the bosonic open string. It is a generalization of the loop variable approach that was used earlier for the free, and lowest order interacting cases. The…
The goal of this paper is twofold. In the first part we discuss a general approach to determine Lyapunov exponents from ensemble- rather than time-averages. The approach passes through the identification of locally stable and unstable…
We show that in the classical interaction picture the echo-dynamics, namely the composition of perturbed forward and unperturbed backward hamiltonian evolution, can be treated as a time-dependent hamiltonian system. For strongly chaotic…
Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7)…
The partition function of a system of galaxies in gravitational interaction can be cast in an Ising Model form, and this reformulated via a Hubbard--Stratonovich transformation into a three dimensional stochastic and classical scalar field…
Various kinematical quantities associated with the statistical properties of dynamical systems are examined: statistics of the motion, dynamical bases and Lyapunov exponents. Markov partitons for chaotic systems, without any attempt at…
In this paper, we give a quantitative estimate for the sum of the first $N$ Lyapunov exponents for random perturbations of a natural class $2N$-dimensional volume-preserving systems exhibiting strong hyperbolicity on a large but…
The statistical behaviour of a product of independent, identically distributed random matrices in $\text{SL}(2,{\mathbb R})$ is encoded in the generalised Lyapunov exponent $\Lambda$; this is a function whose value at the complex number $2…
We present new estimate for Hardy-type inequality in variable exponent Lebesgue spaces. More precisely, by imposing regularity assumptions on the exponent, we prove that the estimations can be reduced to the fixed exponents.
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
We study numerically the thermal conductivity coefficient $\kappa$ as a function of system length $L$ for several different quasi one dimensional models: classical gases of hard spheres with both longitudinal and transverse degrees of…
In this article we study if a Deep Learning technique can be used to obtain an approximated value of the Lyapunov exponents of a dynamical system. Moreover, we want to know if Machine Learning techniques are able, once trained, to provide…
Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when…
We study Lyapunov exponents of tracers in compressible homogeneous isotropic turbulence at different turbulent Mach number $M_t$ and Taylor-scale Reynolds number $Re_\lambda$. We demonstrate that statistics of finite-time Lyapunov exponents…
We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
Linear perturbations of solutions of dynamical systems exhibit different asymptotic growth rates, which are naturally characterized by so-called covariant Lyapunov vectors (CLVs). Due to an increased interest of CLVs in applications,…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…
We study the Lyapunov instability of a two-dimensional fluid composed of rigid diatomic molecules, with two interaction sites each, and interacting with a WCA site-site potential. We compute full spectra of Lyapunov exponents for such a…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…