Introduction to Dynamical Systems

  • Yuri A. Kuznetsov
Part of the Applied Mathematical Sciences book series (AMS, volume 112)


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.


State Space Phase Portrait Evolution Operator Monodromy Matrix Vertical Strip 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Yuri A. Kuznetsov
    • 1
    • 2
  1. 1.Centrum voor Wiskunde en InformaticaAmsterdamThe Netherlands
  2. 2.Institute of Mathematical Problems of BiologyRussian Academy of SciencesPushchino, Moscow RegionRussia

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