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 Trudy Mat. Inst. Steklova, 2020, Volume 310, Pages 78–85 (Mi tm4104)

On Integrability of Dynamical Systems

I. V. Volovich

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: A classical dynamical system may have smooth integrals of motion and not have analytic ones; i.e., the integrability property depends on the category of smoothness. Recently it has been shown that any quantum dynamical system is completely integrable in the category of Hilbert spaces and, moreover, is unitarily equivalent to a set of classical harmonic oscillators. The same statement holds for classical dynamical systems in the Koopman formulation. Here we construct higher conservation laws in an explicit form for the Schrödinger equation in the multidimensional space under various fairly wide conditions on the potential.

DOI: https://doi.org/10.4213/tm4104

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 310, 70–77

Bibliographic databases:

UDC: 517.958:530.145
Revised: January 19, 2020
Accepted: May 8, 2020

Citation: I. V. Volovich, “On Integrability of Dynamical Systems”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 78–85; Proc. Steklov Inst. Math., 310 (2020), 70–77

Citation in format AMSBIB
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