 00519 Lazutkin V.F
 A remark on ``Some remarks on the problem of ergodicity of the
Standard Map''
(13K, LATeX 2e)
Dec 30, 00

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Abstract. We consider the standard family
$F_g:(x,y)\mapsto (g\cos(2\pi x)y,x)$ of areapreserving maps
defined on the twotorus ${\bf R}^2/{\bf Z}^2\,,$
the parameter $g$ ranging along the real axis ${\bf R}\,.$
We prove that there exists a subset ${\cal E}\subset{\bf R}$ whose density
tends to zero along the real axis, such that for any $g$ in the complement to
${\cal E}$ the map $F_g$ is ergodic an has nonzero
Lyapunov exponents almost everywhere
in ${\bf R}^2/{\bf Z}^2$ with respect to the Haar measure.
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