Frequency-domain Methods For Nonlinear Analysis: Theory And Applications

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This book deals with the investigation of global attractors of nonlinear dynamical systems. The exposition proceeds from the simplest attractor of a single equilibrium to more comp licated ones, i.e. to finite, denumerable and continuum equilibria sets; and further, to cycles, homoclinic and heteroclinic orbits; and finally, to strange attractors consisting of irregular unstable trajectories. On the complicated equilibria sets, the methods of Lyapunov stability theory are transferred. They are combined with stability techniques specially elaborated for such sets. The results are formulated as frequency-domain criteria. The methods connected with the theorems of existence of cycles and homoclinic orbits are developed. The estimates of Hausdorff dimensions of attractors are presented.Format: HardcoverNo of Pages: 512Imprint: World ScientificPublication date: 19960501Series: World Scientific Series On Nonlinear Science Series A Show more