How Expansivity is 3 times of linear expasitivity?

Answer 1

Expansivity is a concept in dynamical systems that indicates how sensitive a system is to initial conditions, often measured by the rate at which trajectories diverge. When we say that expansivity is three times that of linear expansitivity, it suggests that the rate at which nearby trajectories separate in the expansive system is three times greater than in the linear case. This can imply a more chaotic or unpredictable behavior in the expansive system compared to the linear one, where the separation rate is constant and less sensitive to initial variations. Thus, this comparison highlights the heightened sensitivity of the expansive system relative to a linear framework.