Symbolic Partition In Chaotic Maps

Symbolic dynamics is a very effective description of chaotic motion which captures the robust topological feature but ignores coordinate-dependent metric properties of a system.However,it is difficult to produce a good symbolic parti-tion,especially in high dimensions where the stable and unstable manifolds get entangled in a complex manner.In this thesis,we propose a new scheme which only focus on the unstable manifold but not disturbed by the high-dimensional stable manifold and detects partition boundaries by locating folding points at different levels that makes our method can be extend to high-dimensional maps.Finally,we successfully apply it to chaotic maps with one-dimensional unsta-ble direction:the Hénon map with different parameter values and a well-known three-dimensional map,with the hope that the technique could be extended to more general situations.