Cyclicity of some analytic maps

Matej Mencinger, Brigita Ferčec, Regilene Oliveira and Dušan Pagon

Applied Mathematics and Computation, 2017, vol. 295, issue C, 114-125

Abstract: In this paper, we describe an approach to estimate the cyclicity of centers in maps given by f(x)=−x−∑k=1∞akxk+1. The main motivation for this problem originates from the study of cyclicity of planar systems of ODEs. We also consider the bifurcation of limit cycles from each component of the center variety of some particular cases of maps f(x)=−x−∑k=1∞akxk+1 arising from algebraic equations of the form x+y+h.o.t.=0 where higher order terms up to degree four are present.

Keywords: Discrete dynamical systems; Polynomial maps; Periodic points; Limit cycles; Cyclicity (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:295:y:2017:i:c:p:114-125

DOI: 10.1016/j.amc.2016.09.026

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