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 TMF, 1972, Volume 11, Number 3, Pages 344–353 (Mi tmf2874)

On groups that correspond to the simplest problems of classical mechanics

È. È. Shnol'

Abstract: 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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English version:
Theoretical and Mathematical Physics, 1972, 11:3, 557–564

Bibliographic databases:

Citation: È. È. Shnol', “On groups that correspond to the simplest problems of classical mechanics”, TMF, 11:3 (1972), 344–353; Theoret. and Math. Phys., 11:3 (1972), 557–564

Citation in format AMSBIB
\Bibitem{Shn72} \by \E.~\E.~Shnol' \paper On groups that correspond to the simplest problems of classical mechanics \jour TMF \yr 1972 \vol 11 \issue 3 \pages 344--353 \mathnet{http://mi.mathnet.ru/tmf2874} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=475376} \zmath{https://zbmath.org/?q=an:0241.70025} \transl \jour Theoret. and Math. Phys. \yr 1972 \vol 11 \issue 3 \pages 557--564 \crossref{https://doi.org/10.1007/BF01028372}