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＜電子ブック＞
Frequency Methods in Oscillation Theory / by G.A. Leonov, I.M. Burkin, A.I. Shepeljavyi
(Mathematics and Its Applications ; 357)

版	1st ed. 1996.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1996
本文言語	英語
大きさ	XII, 404 p : online resource
著者標目	*Leonov, G.A author Burkin, I.M author Shepeljavyi, A.I author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Fourier analysis LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Mathematics FREE:Differential Equations FREE:Fourier Analysis FREE:Global Analysis and Analysis on Manifolds FREE:Applications of Mathematics
一般注記	1. Classical two-dimensional oscillating systems and their multidimensional analogues -- §1.1. The van der Pol equation -- §1.2. The equation of oscillations of a pendulum -- §1.3. Oscillations in two-dimensional systems with hysteresis -- §1.4. Lower estimates of the number of cycles of a two-dimensional system -- 2. Frequency criteria for stability and properties of solutions of special matrix inequalities -- §2.1. Frequency criteria for stability and dichotomy -- §2.2. Theorems on solvability and properties of special matrix inequalities -- 3. Multidimensional analogues of the van der Pol equation -- §3.1. Dissipative systems. Frequency criteria for dissipativity -- §3.2. Second-order systems. Frequency realization of the annulus principle -- §3.3. Third-order systems. The torus principle -- §3.4. The main ideas of applying frequency methods for multidimensional systems -- §3.5. The criterion for the existence of a periodic solution in a system with tachometric feedback -- §3.6. The method of transition into the "space of derivatives" -- §3.7. A positively invariant torus and the function "quadratic form plus integral of nonlinearity" -- §3.8. The generalized Poincaré–Bendixson principle -- §3.9. A frequency realization of the generalized Poincaré-Bendixson principle -- §3.10. Frequency estimates of the period of a cycle -- 4. Yakubovich auto–oscillation -- §4.1. Frequency criteria for oscillation of systems with one differentiable nonlinearity -- §4.2. Examples of oscillatory systems -- 5. Cycles in systems with cylindrical phase space -- §5.1. The simplest case of application of the nonlocal reduction method for the equation of a synchronous machine -- §5.2. Circular motions and cycles of the second kind in systems with one nonlinearity -- §5.3. The method ofsystems of comparison -- §5.4. Examples -- §5.5. Frequency criteria for the existence of cycles of the second kind in systems with several nonlinearities -- §5.6. Estimation of the period of cycles of the second kind -- 6. The Barbashin-Ezeilo problem -- §6.1. The existence of cycles of the second kind -- §6.2. Bakaev stability. The method of invariant conical grids -- §6.3. The existence of cycles of the first kind in phase systems -- §6.4. A criterion for the existence of nontrivial periodic solutions of a third-order nonlinear system -- 7. Oscillations in systems satisfying generalized Routh-Hurwitz conditions. Aizerman conjecture -- §7.1. The existence of periodic solutions of systems with nonlinearity from a Hurwitzian sector -- §7.2. Necessary conditions for global stability in the critical case of two zero roots -- §7.3. Lemmas on estimates of solutions in the critical case of one zero root -- §7.4. Necessary conditions for absolute stability of nonautonomous systems -- §7.5. The existence of oscillatory and periodic solutions of systems with hysteretic nonlinearities -- 8. Frequency estimates of the Hausdorff dimension of attractors and orbital stability of cycles -- §8.1. Upper estimates of the Hausdorff measure of compact sets under differentiable mappings -- §8.2. Estimate of the Hausdorff dimension of attractors of systems of differential equations -- §8.3. Global asymptotic stability of autonomous systems -- §8.4. Zhukovsky stability of trajectories -- §8.5. A frequency criterion for Poincaré stability of cycles of the second kind -- §8.6. Frequency estimates for the Hausdorff dimension and conditions for global asymptotic stability HTTP:URL=https://doi.org/10.1007/978-94-009-0193-3

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