V. S. Dryuma, “Geometrical properties of the multidimensional nonlinear differential equations and the finsler metrics of phase spaces of dynamical systems”, TMF, 99:2 (1994), 241–249; Theoret. and Math. Phys., 99:2 (1994), 555

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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 99, Number 2, Pages 241–249 (Mi tmf1583)

This article is cited in 13 scientific papers (total in 13 papers)

Geometrical properties of the multidimensional nonlinear differential equations and the finsler metrics of phase spaces of dynamical systems

V. S. Dryuma

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

Full-text PDF (800 kB) Citations (13)

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Abstract: The multidimensional nonlinear differential equations arising from special conditions on curvature tensor of 3- and 4-dimensional manifolds are considered. The examples of the Finsler metrics, associated with nonlinear dynamical systems are constructed.

English version:
Theoretical and Mathematical Physics, 1994, Volume 99, Issue 2, Pages 555–561
DOI: https://doi.org/10.1007/BF01016138

Bibliographic databases:

Language: English

Citation: V. S. Dryuma, “Geometrical properties of the multidimensional nonlinear differential equations and the finsler metrics of phase spaces of dynamical systems”, TMF, 99:2 (1994), 241–249; Theoret. and Math. Phys., 99:2 (1994), 555–561

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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\pages 555--561

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Linking options:

https://www.mathnet.ru/eng/tmf1583

https://www.mathnet.ru/eng/tmf/v99/i2/p241

This publication is cited in the following 13 articles:

R. C. Kulaev, A. B. Shabat, Trends in Mathematics, Operator Theory and Differential Equations, 2021, 79
R. Ch. Kulaev, A. B. Shabat, “Darboux system and separation of variables in the Goursat problem for a third order equation in $\mathbb {R}^3$”, Russian Math. (Iz. VUZ), 64:4 (2020), 35–43
R. Ch. Kulaev, A. K. Pogrebkov, A. B. Shabat, “Darboux system: Liouville reduction and an explicit solution”, Proc. Steklov Inst. Math., 302 (2018), 250–269
Viorel Badescu, Understanding Complex Systems, Modeling Thermodynamic Distance, Curvature and Fluctuations, 2016, 3
T Yajima, H Nagahama, “KCC-theory and geometry of the Rikitake system”, J. Phys. A: Math. Theor., 40:11 (2007), 2755
V. S. Dryuma, “Toward a Theory of Spaces of Constant Curvature”, Theoret. and Math. Phys., 146:1 (2006), 34–44
Dryuma V., “The Riemann and Einstein-Weyl geometries in the theory of ordinary differential equations their applications and all that”, New Trends in Integrability and Partial Solvability, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 132, 2004, 115–156
Valerii Dryuma, New Trends in Integrability and Partial Solvability, 2004, 115
Valerii Driuma, Maxim Pavlov, “On initial value problem in theory of the second order differential equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, no. 2, 51–58
V. V. Dmitrieva, “Point-Invariant Classes of Third-Order Ordinary Differential Equations”, Math. Notes, 70:2 (2001), 175–180
R. A. Sharipov, “Newtonian normal shift in multidimensional Riemannian geometry”, Sb. Math., 192:6 (2001), 895–932
V. S. Dryuma, “Applications of Riemannian and Einstein–Weyl Geometry in the Theory of Second-Order Ordinary Differential Equations”, Theoret. and Math. Phys., 128:1 (2001), 845–855
Lapo Casetti, Marco Pettini, E.G.D. Cohen, “Geometric approach to Hamiltonian dynamics and statistical mechanics”, Physics Reports, 337:3 (2000), 237

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	71
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