José S Cánovas, Houssem Eddine Rezgui
In this paper, we study the role of geometry in q-deformations. We consider two conjugate maps fa(x) and 1 - fa(1 - x), where fa is the logistic family, with a ∈ (0, 4], and prove that their q-deformations by the map ϕq(x)=qx-q-xq-q-1 may exhibit quite different dynamic behaviors. Thus, the geometry of the maps is more important than their being conjugate when q-deformations are considered.