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Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions
- Source :
- Complexity, Vol 2017 (2017)
- Publication Year :
- 2017
- Publisher :
- Wiley, 2017.
-
Abstract
- 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 l2 displays chaotic dynamics. Here we construct the corresponding operator C on the space of 2π-periodic odd functions and provide its representation involving a Principal Value Integral. We explicitly calculate the eigenfunction of this operator, as well as its periodic points. We also provide examples of chaotic and unbounded trajectories of C.
- Subjects :
- Electronic computers. Computer science
QA75.5-76.95
Subjects
Details
- Language :
- English
- ISSN :
- 10762787 and 10990526
- Volume :
- 2017
- Database :
- Directory of Open Access Journals
- Journal :
- Complexity
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.902d18e045641a29f85c4dd144bd4cb
- Document Type :
- article
- Full Text :
- https://doi.org/10.1155/2017/6020213