Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 3, pp. 344-353
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È. È. Shnol'. On groups that correspond to the simplest problems of classical mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 3, pp. 344-353. http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a7/
@article{TMF_1972_11_3_a7,
author = {\`E. \`E. Shnol'},
title = {On groups that correspond to the simplest problems of classical mechanics},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {344--353},
year = {1972},
volume = {11},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a7/}
}
TY - JOUR
AU - È. È. Shnol'
TI - On groups that correspond to the simplest problems of classical mechanics
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 1972
SP - 344
EP - 353
VL - 11
IS - 3
UR - http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a7/
LA - ru
ID - TMF_1972_11_3_a7
ER -
%0 Journal Article
%A È. È. Shnol'
%T On groups that correspond to the simplest problems of classical mechanics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1972
%P 344-353
%V 11
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a7/
%G ru
%F TMF_1972_11_3_a7
The following questions are discussed: 1) what is the maximum possible complexity of a finite-dimensional group $\mathscr{G}$ of “latent” symmetry? 2) does the existence of a complete set of single-valued integrals of motion always imply the existence of a nontrivial group $\mathscr{G}$? The impossibility of essential extension of the groups $\mathscr{G}$ for known examples is proved; a negative answer is given to the second question.
