Poincaré's program for the global analysis of a dynamical system starts by considering
simple solutions, such as equilibria and periodic orbits, together with their corresponding …

We consider a one-parameter family of area preserving maps in a neighbourhood of an
elliptic fixed point. As the parameter evolves hyperbolic and elliptic periodic orbits of different …

We study the Gevrey character of a natural parameterization of one dimensional invariant
manifolds associated to a parabolic direction of fixed points of analytic maps, that is, a …

In this paper we study the existence and regularity of stable manifolds associated to fixed
points of parabolic type in the differentiable and analytic cases, using the parametrization …

Normal form procedure This is the stepwise 'simplification'by changes of coordinates, of the
Taylor series at an equilibrium point, or of similar series at periodic or quasi-periodic …

In this paper we describe a unified framework for the computation of power series
expansions of invariant manifolds and normal forms of vector fields, and estimate the …

We study normal forms of isolated singularities of vector fields in Rn or Cn. When all
eigenvalues of the linear part of the vector field are nonzero, one can eliminate all so-called …

Abstract The planar (n+ 1)(n+ 1)-body problem models the motion of n+ 1 n+ 1 bodies in the
plane under their mutual Newtonian gravitational attraction forces. When n ≥ 3 n≥ 3, the …

Many theoretical results, the related algorithms and implementations for careful simulations
and a wide range of applications have been obtained up to now. But still many key …

We consider a singular perturbation for a family of analytic symplectic maps of the annulus
possessing a KAM torus. The perturbation introduces dissipation and contains an adjustable …