Geodesic
A transformation of the circle
Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 205-216

Voir la notice de l'article provenant de la source Math-Net.Ru

An investigation of the transformation $T: x\to\lambda\sin x\pmod\pi$ of a circle, which corresponds to a phase transformation encountered in some problems concerning nonlinear vibrations, is carried out. It is proved that if $\lambda=q\pi$ where $q$ is a nonzero integer, there is a measure invariant under the transformation and absolutely continuous with respect to Lebesgue measure. 
@article{MZM_1970_8_2_a8,
     author = {L. A. Bunimovich},
     title = {A transformation of the circle},
     journal = {Matemati\v{c}eskie zametki},
     pages = {205--216},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a8/}
}
TY  - JOUR
AU  - L. A. Bunimovich
TI  - A transformation of the circle
JO  - Matematičeskie zametki
PY  - 1970
SP  - 205
EP  - 216
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a8/
LA  - ru
ID  - MZM_1970_8_2_a8
ER  - 
%0 Journal Article
%A L. A. Bunimovich
%T A transformation of the circle
%J Matematičeskie zametki
%D 1970
%P 205-216
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a8/
%G ru
%F MZM_1970_8_2_a8
L. A. Bunimovich. A transformation of the circle. Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 205-216. http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a8/