The Problem of Positive Kolmogorov-Sinai entropy for the Standard map

Abstract

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 entropy of Tλ sin should be positive. This approach was based on an idea of M. Herman using subharmonic estimates.

Cite this paper

@inproceedings{Knill2005ThePO, title={The Problem of Positive Kolmogorov-Sinai entropy for the Standard map}, author={Oliver Knill}, year={2005} }