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51.
A dynamical system is studied in the neighborhood of an invariant toroidal manifold for the most general relationship between the dimensionality of the phase space and the dimensionality of the manifold.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1399–1408, October, 1994. 相似文献
52.
V. G. Samoilenko 《Ukrainian Mathematical Journal》1994,46(8):1145-1156
We study quasiinvariant deformations of invariant submanifolds of nonlinear Hamiltonian dynamical systems and their small perturbations.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 1043–1054, August, 1994. 相似文献
53.
All irreducible* -representations of the involutive algebraA generated by the so-called Heisenberg relations for the quantum deformation of the group of motions of the Euclidean plane are described.Dedicated to the 70th birthday of our teacher, Prof. Yu. M. BerezanskiiPublished in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 689–692, May, 1995.This research was partially supported by the Ukrainian State Committee on Science and Technology, the International Science Foundation, grant No. U6D000, and a grant from the American Mathematical Society. 相似文献
54.
A constructive approach to the determination of an approximate solution of a boundary value problem with nonlinear boundary conditions g[z (0), z (T)]=0 is proposed. Existence of the exact solution is proved, and error estimates for the constructed approximate solution are provided.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 951–957, July, 1990. 相似文献
55.
56.
We investigate classes of linear extensions of dynamical systems on a torus for which the Lyapunov functions exist for an arbitrary flow on the torus. Linear extensions for which the Lyapunov functions exist only with varying coefficients are considered separately. We investigate the problem of preservation of regularity under perturbation of phase variables. 相似文献
57.
58.
For oscillation resonance systems with delay on a finite segment or a semiaxis, we justify the averaging method with respect to fast variables. We also obtain error estimates for this method, which explicitly depend on a small parameter. 相似文献
59.
60.
A. M. Samoilenko 《Ukrainian Mathematical Journal》2011,63(2):278-314
We consider problems of the linear theory of systems of ordinary differential equations related to the investigation of invariant
hyperplanes of these systems, the notion of equivalence for these systems, and the Floquet–Lyapunov theory for periodic systems
of linear equations. In particular, we introduce the notion of equivalence of systems of linear differential equations of
different orders, propose a new formula of the Floquet form for periodic systems, and present the application of this formula
to the introduction of amplitude–phase coordinates in a neighborhood of a periodic trajectory of a dynamical system. 相似文献