Chaotic Behavior of Autonomous Time-Discrete 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 3 in Dynamical Systems, 2010, pp 149-193 from Springer

Abstract: Abstract Let $$ f : X \rightarrow X $$ be a continuous mapping of a metric space X into itself. Then by the definition 3.1 $$ \pi \left( {x, n} \right) = f^n (x) \quad {\rm for\, all} \quad {x} \in {X} \quad {\rm and} \quad n \in {\mathbb N}_0 $$ with 3.2 $$ f^0 (x) = x \quad {\rm and} \quad f^{n + 1} (x) = f(f^n (x)), \quad n \in {\mathbb N}_0 ,$$ we obtain an autonomous time-discrete dynamical system (see Section 1.3.1).

Keywords: Continuous Mapping; Closed Interval; Chaotic Behavior; Chaotic Mapping; Strange Attractor (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-13722-8_3

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