Abstract
The integrability of certain classes of homogeneous dynamical systems on the tangent bundles of four-dimensional manifolds is shown. The force fields involved in the systems lead to dissipation of variable sign and generalize previously considered fields.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
M. V. Shamolin, Russ. Math. Surv. 53 (3), 637–638 (1998).
M. V. Shamolin, Dokl. Phys. 62 (5), 262–265 (2017).
M. V. Shamolin, Dokl. Phys. 63 (3), 132–137 (2018).
V. V. Kozlov, J. Appl. Math. Mech. 79 (3), 209–216 (2015).
F. Klein, Vorlesungen über nicht-euklidische Geometrie (VDM, Müller, Saarbrücken, 2006).
H. Weyl, Symmetry (Princeton Univ. Press, Princeton, N.J., 2016).
V. V. Kozlov, Russ. Math. Surv. 38 (1), 1–76 (1983).
H. Poincaré, Sur les Courbes Definies par les Equations Differentielles: Oeuvres (Gauthier-Villars, Paris, 1951), Vol. 1.
E. Kamke, Gewohnliche Differentialgleichungen, 5th ed. (Akademie-Verlag, Leipzig, 1959).
V. V. Trofimov, and M. V. Shamolin, J. Math. Sci. 180 (4), 365–530 (2012).
M. V. Shamolin, Dokl. Phys. 63 (10), 424–429 (2018).
B. V. Shabat, Introduction to Complex Analysis (Nauka, Moscow, 1987; Am. Math. Soc. Providence, R.I., 1992).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by I. Ruzanova
Rights and permissions
About this article
Cite this article
Shamolin, M.V. New Cases of Homogeneous Integrable Systems with Dissipation on Tangent Bundles of Four-Dimensional Manifolds. Dokl. Math. 103, 85–91 (2021). https://doi.org/10.1134/S1064562421020046
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562421020046