Abstract
In the current paper we suggest a new robust algorithm to search for cycles of arbitrary length in non-linear autonomous discrete dynamical systems. With the help of the computer we were able to find (unstable) cycles for several basic maps of nonlinear science: Hénon, Holmes cubic, Ikeda, Lozi, Elhaj-Sprott. The theoretical part of the paper is based on properties of a new family of extremal polynomials that contains the Fejér and Suffridge polynomials. The associated combination of geometric complex analysis and discrete dynamics seems to be a new phenomenon, both theoretical and practical. A novelty of this paper is in the discovery of a close connection between two seemingly disconnected fields: extremal polynomials and cycles in dynamical systems.
Original language | English |
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Pages (from-to) | 603-626 |
Number of pages | 24 |
Journal | New York Journal of Mathematics |
Volume | 25 |
State | Published - 2019 |
Keywords
- Chaos control
- Discrete dynamical systems
- Extremal polynomials