  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.

Dynamical Systems;Spectral Theory