Complexity in linear systems: a chaotic linear operator on the space of odd \(2 \pi\)-periodic functions
type: Item
instance of: scholarly article
title: Complexity in linear systems: a chaotic linear operator on the space of odd \(2 \pi\)-periodic functions
zbMATH Open document ID: 1367.93267
DOI: 10.1155/2017/6020213
author: Tamás Kalmár-Nagy
author: Márton Kiss
published in: Complexity
publication date: 2017-08-03T00:00:00Z
review text: Summary: Not just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. It has long been known that twice the backward shift on the space of square-summable sequences \(l_2\) displays chaotic dynamics. Here we construct the corresponding operator \(\mathcal{C}\) on the space of \(2 \pi\)-periodic odd functions and provide its representation involving a Principal Value Integral. We explicitly calculate the eigenfunctions of this operator, as well as its periodic points. We also provide examples of chaotic and unbounded trajectories of \(\mathcal{C}\).
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93B60
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 6755985
zbMATH Keywords: infinite-dimensional linear systems
zbMATH Keywords: complex behavior
zbMATH Keywords: chaotic dynamics
zbMATH Keywords: principal value integral
zbMATH Keywords: eigenfunctions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/6020213
OpenAlex ID: W2591071698
Wikidata QID: Q59142925
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description: scientific article; zbMATH DE number 6755985