A modified digraph cell mapping method

Abstract

By introducing new concepts, this paper presents a new classification of transient cells for the digraph cell mapping dynamical system. Based on this new classification, the approximation problem of the invariant manifolds of dynamical system is discussed in detail. In order to improve the efficiency and speed of computing, an effective algorithm is given to complete the above classification. As an illustrative example, Henon map is taken to demonstrate the validity of the modified digraph cell mapping method.