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Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2020 Volume 187, Pages 68–81 (Mi into733)

Examples of nine-order integrable dynamical systems with dissipation

M. V. Shamolin

Lomonosov Moscow State University

Abstract: In this paper, the integrability of some classes of homogeneous with respect to a part of variables ninth-order dynamical systems, in which a system on the tangent bundle to four-dimensional manifolds is distinguished. In this case, force fields have a dissipation of different signs and are generalizations of those considered earlier.

Keywords: dynamical system, nonconservative force fields, integrability, transcendental first integral.

UDC: 517, 531.01

MSC: 58-xx, 70-xx

DOI: 10.36535/0233-6723-2020-187-68-81


 English version:
Journal of Mathematical Sciences (New York), 2025, 287:5, 754–766

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© Steklov Math. Inst. of RAS, 2025