Titlebook: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields; John Guckenheimer,Philip Holmes Book 1983 Springer Science+B

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Introduction: Differential Equations and Dynamical Systems,w some of the better-known results on two-dimensional autonomous systems and end with a statement and sketch of the proof of Peixoto’s theorem, an important result which summarizes much of our knowledge of two-dimensional flows.

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Local Bifurcations,ters 6 and 7, a systematic theory which describes and permits the analysis of the typical bifurcations one encounters. We pay careful attention to the examples introduced in Chapter 2 and use these to illustrate the theory that we present.

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978-1-4612-7020-1Springer Science+Business Media New York 1983

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John Guckenheimer,Philip HolmesIncludes supplementary material:

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Global Bifurcations,In Chapter 3 we dealt with the local bifurcation properties of equilibrium points and periodic orbits. The theory developed there relied upon coordinate transformations which bring general systems into normal forms, from which dynamical information can be deduced from the Taylor series of a vector field or map at a single point.

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