We show that planar continuous alternating systems, which can be used to model systems with seasonality, can exhibit a type of Parrondo's dynamic paradox, in which the stability of an equilibrium, common to all seasons is ...

We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction ...

We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful ...

t Let F be a real or complex n-dimensional map. It is said that F is globally periodic if there exists some p ∈ N + such that Fp(x) = x for all x, where F k = F ◦ F k−1, k ≥ 2. The minimal p satisfying this property is ...

We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of K, where K is ℝ or ℂ, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary ...

This paper studies non-autonomous Lyness-type recurrences of the form x n+2 = (a n + x n+1)/x n , where {a n } is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k {1, 2, 3, ...

We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ...

We consider the problem of characterizing, for certain natural number m, the local C^m-non-integrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this non-integrability ...

We describe the sequences {xn}n given by the non-autonomous second-order Lyness difference equations xnþ2 ¼ ðan þ xnþ1Þ=xn, where {an}n is either a 2-periodic or a 3- periodic sequence of positive values and the initial ...

We study the dynamics of the piecewise planar rotations F¿(z)=¿(z-H(z)), with z¿C , H(z)=1 if Im(z)=0, H(z)=-1 if Im(z)<0, and ¿=eia¿C , being a a rational multiple of p. Our main results establish the dynamics in the so ...