2019/05/02 by Vivas, Liz
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1905.00937
Let f(z) = z+z2+O(z3) and fε(z) = f(z) + ε2. A classical result in parabolic bifurcation in one complex variable is the following: if N-\fracπε→ 0 we obtain (fε)N → Lf, where Lf is the Lavaurs map of f. In this paper we study a non-autonomous parabolic bifurcation. We focus on the case of f0(z)=(z)/(1-z). Given a sequence \εi\1≤ i≤ N, we denote fn(z) = f0(z) + εn2. We give sufficient and necessary conditions on the sequence \εi\ that imply that fN∘… f1 → \textrmId (the Lavaurs map of f0). We apply our results to prove parabolic bifurcation phenomenon in two dimensions for some class of maps.