Construction of mappings with attracting cycles

✍ Scribed by Weinian Zhang; R.P. Agarwal

• Book ID: 104352491
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 368 KB
• Volume: 45
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(03)00088-9

✦ Synopsis

In (11, two methods to construct polynomial mappings with periodic points are given with Lagrange interpolation and Newton interpolation, and a conjecture that such polynomial mappings with chaotic behaviors should be a "generalized primitive polynomial" is raised. In this paper, we additionally consider stability of periodic points and give a new method to construct polynomial mappings with attracting cycles or superstable cycles. Based on this construction, we show how to further construct a mapping which is not in polynomial forms but possesses the same periodicity. We also discuss properties of such polynomials with integer cycles. Finally, we point out a falsity in [l] and give counterexamples against the conjecture in [l].