An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Then we have the following Morse lemma. Lemma 14.8.3 (Morse) If F is a Cr, r ≥ 3, or analytic Morse function near x = 0, then in a neighborhood of x = 0 there exists a Cr−2, or analytic diffeomorphism, which transforms F to the form ...
This book introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics.
This book examines qualitative methods for nonlinear differential equations, bifurcation theory and chaos in terms suitable for advanced undergraduate and first-year postgraduate students in mathematics and physics.
tions, in Differential Equations in Mathematical Physics, I. Knowles and Y. Saito (Eds.), Lecture Note in Mathematics, Springer-Verlag, New York, 1985. J. Ginibre and H. Vélo [1] Time decay of finite energy solutions of the nonlinear ...
The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level.
DeAngelis, D. L., L. J. Gross, M. A. Huston, W. F. Wolff, D. M. Fleming, E. J. Comiskey, and S. M. Sylvester. 1998. ... Harvell, C. D., K. Kim, J. M. Burkholder, R. R. Colwell, P. R. Epstein, J. Grimes, E. E. Hofmann, E. K. Lipp, ...
This is a book on nonlinear dynamical systems and their bifurcations under parameter variation.
" Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures.
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject.