Methods for Simplifying Dynamical Systems
When one thinks of simplifying dynamical systems, two approaches come to mind: one, reduce the dimensionality of the system and two, eliminate the nonlinearity. Two rigorous mathematical techniques that allow substantial progress along both lines of approach are center manifold theory and the method of normal forms. These techniques are the most important, generally applicable methods available in the local theory of dynamical systems, and they will form the foundation of our development of bifurcation theory in Chapter 3.
KeywordsVector Field Periodic Orbit Normal Form Invariant Manifold Stable Manifold
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