259 220 Preliminary Results of the Method of A Priori Integral Estimates for

259 220 preliminary results of the method of a priori

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..................................................................................................... 259 2.20 Preliminary Results of the Method of A Priori Integral Estimates for Integro-Differential Equations ..................................................................................................... ..................................................................................................... 264 2.21 Bakaev-Guzh Technique .................................................................. 272 2.22 Non-local Reduction Method ........................................................... 278 2.23 Sharpening of Circle Criterion for Integro-Differential Equations . . 292 III Circular Solutions and Cycles 307 5 Existence of Circular Solutions and Cycles for Systems Described with Ordinary Differential Equations 309 3.1 Periodic Solutions of a Control System with a Nonlinearity from the Hurwitzian Sector ...................................................................................................... 309 3.1 Periodic Solutions of Dissipative Systems 332 3.2 Pendulum-Like Systems with a Single Sign-Constant Nonlinearity 346 3.2 Existence of Circular Solutions and Cycles of the Second Kind of Pendulum-Like Systems ...................................................................................................... 348 3.3 Circular Solutions and Cycles of the Second Kind in Concrete Systems 358 3.4 Estimation of the Period of a Cycle of the Second Kind 368 3.5 Cycles of the First Kind in the Pendulum-Like Systems
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381 6 Necessary Conditions of Gradient-Like Behavior for the Systems Described by Integro-DifFerential Equations 397 3.8 Frequency-Domain Criterion of Existence of Circular Solutions for an Integro-Differential Equation with a Periodic Nonlinearity ...................................................................................................... 397 3.8 Estimation of the Period of Periodic Solutions of the Second Kind 404 IV Existence of Homoclinic Orbits 415 7 Homoclinic Orbits in Pendulum-Like Systems 417 4.1 Homoclinic Orbits. Preliminary Consideration 417 4.2 Homoclinic Orbits of Pendulum-Like Systems with One Nonlinearity 420 4.3 Dynamics of Synchronous Machines 430 V Dimension of Attractors 437 8 Frequency-Domain Estimates of Hausdorff Dimension of Attractors 439 5.1 Preliminary Considerations 439 5.2 Topological Dimension 442 5.3 Hausdorff Measure and Hausdorff Dimension ............................................................................................................. ............................................................................................................. 445 5.4 Differentiable Mappings: Upper Estimates of Hausdorff Dimension of Compacts ...................................................................................................... ...................................................................................................... 453 5.5 Differential Equations: Upper Estimates of Hausdorff Dimension of Attractors ...................................................................................................... ...................................................................................................... 457 5.4 Frequency-domain Estimates of Hausdorff Dimension of Attractors. 466 Bibliography 477 Index 497
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  • Spring '16
  • Stability theory, Pendulum-Like Systems

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