Some family of center manifolds of a fixed indeterminate point

Abstract

In this article, we study the local dynamical structure of a rational mapping F of P² at a fixed indeterminate point p. In the previous paper, using a sequence of points which is defined by blow-ups, we have constructed an invariant family of holomorphic curves at p. In this paper, using the same sequence of points, we approximate a set of points whose forward orbits stay in a neighborhood of p. Moreover, for a specific rational mapping we construct a family {W_j}_{j ∈ {1,2}^N} of center manifolds of p. The main result of this paper is to give the asymptotic expansion of the defining function of W_j.