Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Problem of Positive Kolmogorov-Sinai entropy for the Standard map   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.

4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc