By G. A. Leonov, I. M. Burkin, A. I. Shepeljavyi (auth.)
This ebook is dedicated to nonlocal conception of nonlinear oscillations. The frequency tools of investigating difficulties of cycle lifestyles in multidimensional analogues of Van der Pol equation, in dynamical structures with cylindrical part area and dynamical structures pleasing Routh-Hurwitz generalized stipulations are systematically offered the following for the 1st time.
to resolve those difficulties equipment of Poincaré map building, frequency tools, synthesis of Lyapunov direct tools and bifurcation thought components are utilized. V.M. Popov's process is hired for acquiring frequency standards, which estimate interval of oscillations. additionally, an method of examine the steadiness of cycles according to the guidelines of Zhukovsky, Borg, Hartmann, and Olech is gifted, and the results showing whilst bounded trajectories are volatile are mentioned. For chaotic oscillations theorems on localizations of attractors are given. the higher estimates of Hausdorff degree and size of attractors generalizing Doudy-Oesterle and Smith theorems are bought, illustrated by way of the instance of a Lorenz procedure and its diverse generalizations.
The analytical gear built within the e-book is utilized to the research of oscillation of assorted keep an eye on structures, pendulum-like platforms and people of synchronization.
Audience: This quantity could be of curiosity to these whose paintings consists of Fourier research, worldwide research, and research on manifolds, in addition to arithmetic of physics and mechanics normally. A historical past in linear algebra and differential equations is thought.