Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Applied Mathematical Sciences #42

by John Guckenheimer, Philip Holmes

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.

Genres: Mathematics, Physics

478 pages, Hardcover

First published August 1, 1983

Reviews

[Michael Weaver]

Guckenheimer and Holmes really explain in systematic detail dynamical system thermal turbulence in planetary interiors and its evolution in time dependent models from that of planetary convection codes. I particularly found the role of k-jets fascinating via the explanation of the mathematical constructions and how those techniques are employed.

[DJ]

apparently THE book on chaos and bifurcation theory