Abstract
In this chapter we introduce the notion of a dynamical system, both for discrete and continuous time. We also describe many examples, including rotations and expanding maps of the circle, endomorphisms and automorphisms of the torus, and autonomous differential equations and their flows. Together with other examples introduced throughout the book, these are used to illustrate new concepts and results. We also describe some basic constructions determining new dynamical systems, including suspension flows and Poincaré maps. Finally, we consider the notion of an invariant set, both for maps and flows.
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References
Barreira, L., Valls, C.: Ordinary Differential Equations: Qualitative Theory. Graduate Studies in Mathematics, vol. 137. Am. Math. Soc., Providence (2012)
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© 2013 Springer-Verlag London
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Barreira, L., Valls, C. (2013). Basic Notions and Examples. In: Dynamical Systems. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-4835-7_2
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DOI: https://doi.org/10.1007/978-1-4471-4835-7_2
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4834-0
Online ISBN: 978-1-4471-4835-7
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