Matematičeskie zametki, Tome 4 (1968) no. 6, pp. 741-750
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Yu. S. Ilyashenko. Density of an individual solution and ergodicity of a family of solutions to the equation $d\eta/d\xi=P(\xi,\,\eta)/Q(\xi,\,\eta)$. Matematičeskie zametki, Tome 4 (1968) no. 6, pp. 741-750. http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a14/
@article{MZM_1968_4_6_a14,
author = {Yu. S. Ilyashenko},
title = {Density of an~individual solution and ergodicity of a~family of solutions to the equation $d\eta/d\xi=P(\xi,\,\eta)/Q(\xi,\,\eta)$},
journal = {Matemati\v{c}eskie zametki},
pages = {741--750},
year = {1968},
volume = {4},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a14/}
}
TY - JOUR
AU - Yu. S. Ilyashenko
TI - Density of an individual solution and ergodicity of a family of solutions to the equation $d\eta/d\xi=P(\xi,\,\eta)/Q(\xi,\,\eta)$
JO - Matematičeskie zametki
PY - 1968
SP - 741
EP - 750
VL - 4
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a14/
LA - ru
ID - MZM_1968_4_6_a14
ER -
%0 Journal Article
%A Yu. S. Ilyashenko
%T Density of an individual solution and ergodicity of a family of solutions to the equation $d\eta/d\xi=P(\xi,\,\eta)/Q(\xi,\,\eta)$
%J Matematičeskie zametki
%D 1968
%P 741-750
%V 4
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a14/
%G ru
%F MZM_1968_4_6_a14
The paper provides a sharpened proof of M. G. Khudai–Verenov's theorem on the density in $C^2$ of solutions to the equation $d\eta/d\xi=F/Q$ on condition that this equation has two singular points at infinity whose characteristic numbers satisfy certain constraints of the incommensurability type.
