Abstract
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.
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© 1995 Springer Science+Business Media New York
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Kuznetsov, Y.A. (1995). Introduction to Dynamical Systems. In: Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, vol 112. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2421-9_1
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DOI: https://doi.org/10.1007/978-1-4757-2421-9_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2423-3
Online ISBN: 978-1-4757-2421-9
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