Knot Theory Based on the Minimal Braid in Lorenz System

Abstract

By means of symbolic dynamics in Lorenz map, after studying spatial topological structure of dynamical knot constructed by the minimal braid assumption, we pry into the spatial structure of three-dimensional manifold from low-dimensional space. Lorenz dynamical knot provides a scheme about suspension. So, we are able to understand partly dynamical behaviors’ topological properties of high-dimensional differential manifold by studying dynamical knot’s properties. We hope to afford an approach and understand the nature of physical reality, especially in the study of DNA sequences, 20 amino acids symbolic sequences of proteid structure, and time series that can be symbolic in finance market et al.