Li-Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology

Li-Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology is introduced. Based on this topology on the Euclidean space, a flow generated from a linear differential equation is proved to be Li-Yorke chaotic under certain conditions, which is in sharp contract to the well-known fact that linear differential equations cannot be chaotic in a finite-dimensional space with a strong topology.