Geodesic
On groups that correspond to the simplest problems of classical mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 3, pp. 344-353

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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. 
@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},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a7/}
}
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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/