Geodesic
On groups that correspond to the simplest problems of classical mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 3, pp. 344-353 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {On groups that correspond to the simplest problems of classical mechanics},
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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/

[1] E. Noether, Nachr. Göttingen, Math. Phys. Kl., 238 (1918); Variatsionnye printsipy mekhaniki, Sb., Fizmatgiz, 1959 | MR

[2] A. I. Baz, Ya. B. Zeldovich, A. M. Perelomov, Rasseyanie, reaktsii i raspady v nerelyativistskoi kvantovoi mekhanike, «Nauka», 1966 | Zbl

[3] M. I. Petrashen, E. D. Trifonov, Primenenie teorii grupp v kvantovoi mekhanike, «Nauka», 1967

[4] V. I. Arnold, Sib. matem. zhurnal, 4 (1963), 471 | MR

[5] E. E. Shnol, Matem. zametki, 5 (1969), 55 | MR | Zbl

[6] L. S. Pontryagin, Nepreryvnye gruppy, gl. 11, GTTI, 1954 | MR

[7] D. P. Zhelobenko, Kompaktnye gruppy Li i ikh predstavleniya, gl. 14, «Nauka», 1970 | MR | Zbl