Uncontrolled Systems

Werner Krabs and Stefan Pickl ()
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Werner Krabs: Technical University of Darmstadt, Department of Mathematics
Stefan Pickl: Universität der Bundeswehr München, Department of Computer Science

Chapter 1 in Dynamical Systems, 2010, pp 1-75 from Springer

Abstract: Abstract The concept of dynamical systems has developed out of the qualitative theory of differential equations which was established by Lyapunov and Poincaré in the course of the two last decades of the nineteenth century. As final result of a development which lasted more than half a century the following abstract definition of a dynamical system has grown out: Let X be a metric space with metric d. Further let I be an additive semigroup of real numbers, i.e. a subset I of $$\mathbb{R}$$ with $$\begin{array} {rlr} 0 \in I, & {}\\ t,s \in I & \Rightarrow t + s = s + t \in I,\\ {t, s, r} \in { I} & \Rightarrow {({t}{ + } s)}{ + }{ r}{ = }{ t + (s + r)} .\\ \end{array} $$

Keywords: Nash Equilibrium; Periodic Orbit; Lyapunov Function; Jacobi Matrix; Negative Real Part (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-13722-8_1

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DOI: 10.1007/978-3-642-13722-8_1

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