The center and cyclicity problems for some analytic maps

Matej Mencinger and Brigita Ferčec

Applied Mathematics and Computation, 2017, vol. 306, issue C, 73-85

Abstract: The center variety and bifurcations of limit cycles from the center for maps f(x)=−∑k=0∞akxk+1 arising from x+y+∑j=0nαn−j,jxn−jyj=0are considered. Motivated by a general result for n=2ℓ+1 we investigate the center and cyclicity problem for n being even. We review results for n=2 and n=4 and perform the analysis for n=6,8,10. Finally, we state some conjectures for general n=2ℓ.

Keywords: Discrete dynamical systems; Polynomial maps; Periodic points; Center variety; Cyclicity (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:306:y:2017:i:c:p:73-85

DOI: 10.1016/j.amc.2017.02.033

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