Matematičeskie zametki, Tome 58 (1995) no. 5, pp. 723-735
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N. G. Moshchevitin. Recurrence of the integral of a smooth three-frequency conditionally periodic function. Matematičeskie zametki, Tome 58 (1995) no. 5, pp. 723-735. http://geodesic.mathdoc.fr/item/MZM_1995_58_5_a7/
@article{MZM_1995_58_5_a7,
author = {N. G. Moshchevitin},
title = {Recurrence of the integral of a~smooth three-frequency conditionally periodic function},
journal = {Matemati\v{c}eskie zametki},
pages = {723--735},
year = {1995},
volume = {58},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_5_a7/}
}
TY - JOUR
AU - N. G. Moshchevitin
TI - Recurrence of the integral of a smooth three-frequency conditionally periodic function
JO - Matematičeskie zametki
PY - 1995
SP - 723
EP - 735
VL - 58
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1995_58_5_a7/
LA - ru
ID - MZM_1995_58_5_a7
ER -
%0 Journal Article
%A N. G. Moshchevitin
%T Recurrence of the integral of a smooth three-frequency conditionally periodic function
%J Matematičeskie zametki
%D 1995
%P 723-735
%V 58
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_5_a7/
%G ru
%F MZM_1995_58_5_a7
We prove V. V. Kozlov's famous conjecture claiming that the integral of an analytic three-frequency conditionally periodic function with zero mean and incommensurable frequencies recurs. For a conditionally periodic function of class $C^2$ on $\mathbb T^n$, $n=2,3$, we prove that the integral recurs uniformly with respect to the initial data.
[5] Moshchevitin N. G., “Recent results on quasiperiodic function integral asymptotic behaviour”, Dynamical Systems of Classical Mechanics, Collection of papers, Advances of Soviet Mathematics, AMS Publ., 1995
[6] Khinchin A. Ya., Tsepnye drobi, Nauka, M., 1978