Special functions created by Borel-Laplace transform of Hénon map

We present a novel class of functions that can describe the stable and unstable manifolds of the Henon map. We propose an algorithm to construct these functions by using the Borel-Laplace transform. Neither linearization nor perturbation is applied in the construction, and the obtained functions are exact solutions of the Henon map. We also show that it is possible to depict the chaotic attractor of the map by using one of these functions without explicitly using the properties of the attractor.