Geodesic
Multiplicative dynamical systems in terms of the~induced dynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 3, pp. 436-444

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We realize an example of induced dynamics using new multiplicative determinant relations whose roots give the particle positions. We present both a general scheme for describing completely integrable dynamical systems parameterized by an arbitrary $N\times N$ matrix of momenta and an explicit model that interpolates between the Calogero–Moser and Ruijsenaars–Schneider hyperbolic systems. We consider some special cases of this model in detail.
Keywords: induced dynamics, completely integrable system. 
@article{TMF_2020_204_3_a7,
     author = {A. K. Pogrebkov},
     title = {Multiplicative dynamical systems in terms of the~induced dynamics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {436--444},
     publisher = {mathdoc},
     volume = {204},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_204_3_a7/}
}
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A. K. Pogrebkov. Multiplicative dynamical systems in terms of the~induced dynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 3, pp. 436-444. http://geodesic.mathdoc.fr/item/TMF_2020_204_3_a7/