Super-attracting cycles for the cosine-root family

D.A. Brown and M.L. Halstead

Chaos, Solitons & Fractals, 2007, vol. 31, issue 5, 1191-1202

Abstract: We investigate the dynamics of the cosine-root family, Cλ(z)=λcosz, where λ∈C. When λ∈R, we focus on the distribution of super-attracting cycles associated to the two critical values. In particular, we locate the parameters leading to super-attracting three cycles for one of the critical values while the other critical value is attracted to a fixed point. These results are used to verify observations made upon viewing Julia and parameter plane pictures.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:31:y:2007:i:5:p:1191-1202

DOI: 10.1016/j.chaos.2005.10.108

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