1995 | OriginalPaper | Chapter
Introduction to Dynamical Systems
Author : Yuri A. Kuznetsov
Published in: Elements of Applied Bifurcation Theory
Publisher: Springer New York
Included in: Professional Book Archive
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This chapter introduces some basic terminology. First, we define a dynamical system and give several examples, including symbolic dynamics. Then we introduce the notions of orbits, invariant sets, and their stability. As we shall see while analyzing the Smale horseshoe, invariant sets can have very complex structures. This is closely related to the fact discovered in the 1960s that rather simple dynamical systems may behave “randomly,” or “chaotically.” Finally, we discuss how differential equations can define dynamical systems of both finite and infinite dimensions.