Research output: Contribution to journal › Article › peer-review
Three-Body Problem in Conformal-Euclidean Space: Complexity of a Low-Dimensional System. / Gevorkyan, A.S.; Bogdanov, A.V.; Mareev, V.V.
In: Physics of Particles and Nuclei, Vol. 56, No. 6, 25.10.2025, p. 1444-1448.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Three-Body Problem in Conformal-Euclidean Space: Complexity of a Low-Dimensional System
AU - Gevorkyan, A.S.
AU - Bogdanov, A.V.
AU - Mareev, V.V.
N1 - Export Date: 01 November 2025; Cited By: 0; Correspondence Address: A.S. Gevorkyan; Institute for Informatics and Automation Problems, National Academy of Sciences of the Republic of Armenia, Armenia; email: g_ashot@sci.am; A.V. Bogdanov; Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, St. Petersburg, Russian Federation; email: a.v.bogdanov@spbu.ru; V.V. Mareev; Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, St. Petersburg, Russian Federation; email: v.mareev@spbu.ru
PY - 2025/10/25
Y1 - 2025/10/25
N2 - Abstract: A general three-body problem is formulated on a curved geometry related to the energy surface of the system of bodies, which allows us to reveal hidden symmetries of the internal motion of a dynamical system and describe it by a system of stiff 6th-order ODEs instead of the usual 8th-order ones. In this formulation, the three-body problem is equivalent to the problem of propagation of a flow of geodesic trajectories on a 3D Riemannian manifold. A new criterion for the divergence of close geodesic trajectories is defined, similar to the Lyapunov exponent only on finite time intervals. Using the stochastic equation of motion of a system of bodies, a second-order partial differential equation of the Fokker-Planck type is derived for the probability distribution of geodesics (PDG) in phase space. Using PDG in a current tube, the entropy of a low-dimensional dynamical system is constructed and its complexity and disequilibrium are estimated. The behavior of new timing parameter (internal time) in global or 3D Jacobi space is studied in detail and its dimension is calculated. © 2025 Elsevier B.V., All rights reserved.
AB - Abstract: A general three-body problem is formulated on a curved geometry related to the energy surface of the system of bodies, which allows us to reveal hidden symmetries of the internal motion of a dynamical system and describe it by a system of stiff 6th-order ODEs instead of the usual 8th-order ones. In this formulation, the three-body problem is equivalent to the problem of propagation of a flow of geodesic trajectories on a 3D Riemannian manifold. A new criterion for the divergence of close geodesic trajectories is defined, similar to the Lyapunov exponent only on finite time intervals. Using the stochastic equation of motion of a system of bodies, a second-order partial differential equation of the Fokker-Planck type is derived for the probability distribution of geodesics (PDG) in phase space. Using PDG in a current tube, the entropy of a low-dimensional dynamical system is constructed and its complexity and disequilibrium are estimated. The behavior of new timing parameter (internal time) in global or 3D Jacobi space is studied in detail and its dimension is calculated. © 2025 Elsevier B.V., All rights reserved.
UR - https://www.mendeley.com/catalogue/43e65f13-6719-3e65-9c15-958f2f173286/
U2 - 10.1134/s1063779625700650
DO - 10.1134/s1063779625700650
M3 - статья
VL - 56
SP - 1444
EP - 1448
JO - Physics of Particles and Nuclei
JF - Physics of Particles and Nuclei
SN - 1063-7796
IS - 6
ER -
ID: 143195215