Chaos and Shadowing

Marat Akhmet ()
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Marat Akhmet: Middle East Technical University, Department of Mathematics

Chapter Chapter 10 in Principles of Discontinuous Dynamical Systems, 2010, pp 155-165 from Springer

Abstract: Abstract The proof of the existence of chaotic attractors remains an important and difficult problem, which is still not resolved fully, even for the Lorentz system [49, 72, 84, 150]. In this chapter, a multidimensional chaosis generated by a special initial value problem for the nonautonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions, and existence of a trajectory, which is dense in the set of all orbits are observed. That is, we concentrate on the topological ingredients of the version proposed by Devaney [62]. An appropriate example is constructed, where a chaotic attractor is indicated, and the intermittency is observed.

Keywords: Special Initial Value Problem; Topological Ingredients; Lorentz System; Chaotic Attractor; Impulsive Differential Equations (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-6581-3_10

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DOI: 10.1007/978-1-4419-6581-3_10

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