When crossing the boundary of stability of a given dynamical system only indicates a bifurcation point and the type of the bifurcating solutions. But it doesn't tell us how and how many new solutions bifurcate or disappear in a bifurcation point. To answer this question one has to take into...

This paper presents a unified framework of different algorithms to numerically compute high order expansions of invariant manifolds associated to a steady state of a dynamical system. The framework is inspired in the parameterization method of Cabré et al. [2003. The parameterization method for...

This paper presents a unified framework of different algorithms to numerically compute high order expansions of invariant manifolds associated to a steady state of a dynamical system. The framework is inspired in the parameterization method of Cabr, Fontich and de la Llave [7], and the...