Written to provide a mathematical bridge between bifurcation and chaos, this text draws on the work of mathematician PoincarT and the Andronov school of nonlinear oscillations to qualitatively study high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented here were developed only recently and have not yet appeared in textbook form. All topics are developed with an introductory background and complete mathematical rigor. The book is for beginning and advanced students of nonlinear dynamics. Shilnikov is affiliated with the Research Institute for Applied Mathematics and Cybernetics in Russia. Annotation c. Book News, Inc., Portland, OR (booknews.com)