Abstract
In this chapter, we introduce and discuss the following fundamental notions that will be used throughout the book: topological equivalence of dynamical systems and theirDynamical systemsclassification of classification, bifurcations and bifurcation diagrams, and topological normal forms for bifurcations. The last section is devoted to the more abstract notion of structural stability. In this chapter we will be dealing only with dynamical systems in the state space $$X={\mathbb R}^n$$ . We would like to study general (qualitative) features of the behavior of dynamical systems, in particular, to classify possible types of their behavior and compare the behavior of different dynamical systems.
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