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

Abstract

The problem of positive Kolmogorov-Sinai entropy of the Chirikov-Standard map 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. This approach was based on an idea of Herman to do subharmonic estimates.This document replaces an announcement I had circulated in 1999. In the present document, the incorrect parts have been deleted. The entropy conjecture is open. The references given in the text might still be helpful for people trying an operator theoretical or analytic approach to this problem in ergodic theory.