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...
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 ...
The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations ...
This is a book on nonlinear dynamical systems and their bifurcations under parameter variation.
As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This second book consists of two chapters (chapters 3 and 4 of the set).
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject.
Vladimir I. Nekorkin. Introduction to Nonlinear Oscillations, First Edition ... Dynamical Systems, International Press, Somerville, MA. Afraimovich, V.S. ... Bifurcations of Planar Vector Fields, Cambridge University Press, Cambridge ...
... Non-linear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer, Berlin, 1983) N.N. Bogolyubov, Yu.A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations (Gordon and Breach/Hindustan Publ., New ...
However , over the past twelve years it has become possible to apply these powerful general ideas to the solution of specific problems , often by interpreting the results of " classical " perturbative and asymptotic computations in a ...
Olver, P. J. (1993). Applications of Lie Groups to Differential Equations. New York, SpringerVerlag. Olver, P. J., and C. Shakiban (2006). Applied Linear Algebra. Upper Saddle River, NJ, Pearson Prentice–Hall. Perko, L. (2000).