Symbolic partition in chaotic maps

In this work, we only use data on the unstable manifold to locate the partition boundaries by checking folding points at different levels, which practically coincide with homoclinic tangencies. The method is then applied to the classic two-dimensional Henon map and a well-known three-dimensional map. Comparison with previous results is made in the Henon case, and Lyapunov exponents are computed through the metric entropy based on the partition to show the validity of the current scheme.