Dynamical Systems can be very complicated. The number of equations, the variables concerned and their interaction with one another may be so intricate as to defy attempts at solution unless ways and means can be found to simplify them. Simplification not only saves effort but also provides intuition. The best known approaches can be grouped under two main headings: reduction of dimensionality and elimination of nonlinearity. In this chapter, we shall briefly review some major ones, starting with the Poincaré map, Floquet theory and proceeding to the Central Manifold theorems, normal forms, elimination of passive coordinates and finally Liapunov-Schmidt reduction. Although these theories are, by nature, advanced, the discussion will be kept at an elementary level.
KeywordsImplicit Function Theorem Fundamental Matrix Floquet Theory Main Heading Economic Student
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