The Boros–Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to their convergence. In the paper, we study the dynamics of a one-parameter family ...

In this paper we study a beyond all orders phenomenon which appears in the analytic unfoldings of the Hopf-zero singularity. It consists in the breakdown of a two-dimensional heteroclinic surface which exists in the truncated ...

In this paper we study the exponentially small splitting of a heteroclinic orbit in some unfoldings of the central singularity also called Hopf-zero singularity. The fields under consideration are of the form: dx dτ = ...

Critical slowing down arises close to bifurcations and involves long transients. Despite slowing down phenomena have been widely studied in local bifurcations i.e., bifurcations of equilibrium points, less is known about ...

In this work, our target is to analyze the dynamics around the $1:-1$ resonance which appears when a family of periodic orbits of a real analytic three-degree of freedom Hamiltonian system changes its stability from ...

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 ...

In this work we consider a normal form around a 1:-1 non semi-simple resonant periodic orbit of a three-degree of freedom Hamiltonian system. From the formal analysis it can be proved the branching off a two-parameter ...

We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We ...

We consider an analytic Hamiltonian system with three degrees of freedom and having a family of periodic orbits with a transition stability complex instability. We reduce the Hamiltonian to a normal form around a transition ...