Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the...

The problem of positive Kolmogorov-Sinai entropy of the Chirikov-Standard map Tλf : (x, y) 7→ (2x − y + λf(x), x) with f(x) = sin(x) with respect to the invariant Lebesgue measure on the two-dimensional is open. In 1999, we believed to have a proof that the entropy can be bounded below by log(λ/2)−C(λ) with C(λ) = arcsinh(1/λ) + log(2/ √ 3) and that for λ > λ0 = (8/(6− 3 √ 3)) = 3.1547..., the ...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 1 June 2020Accepted: 21 May 2021Published online: 26 October 2021KeywordsHamiltonian Monte Carlo, Kolmogorov--Sinai entropy, Markov chain CarloAMS Subject Headings65C05Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industrial and App...

It is popular to study a time-dependent nonlinear system by encoding outcomes of measurements into sequences of symbols following certain symbolization schemes. Mostly, symbolizations by threshold crossings or variants of it are applied, but also, the relatively new symbolic approach, which goes back to innovative works of Bandt and Pompe—ordinal symbolic dynamics—plays an increasing role. In t...

We study chaos in the Hamiltonian Mean Field model (HMF), a system with many degrees of freedom in which N classical rotators are fully coupled. We review the most important results on the dynamics and the thermodynamics of the HMF, and in particular we focus on the chaotic properties. We study the Lyapunov exponents and the Kolmogorov– Sinai entropy, namely their dependence on the number of de...