The Curvature Property of a Linear Dynamical System
Articles > Article ยท 2021
Authors: Tuna BAYRAKDAR, Zahide OK BAYRAKDAR
European Journal of Science and Technology, International, 2021
Summary
In this work a two-dimensional smooth autonomous dynamical system is regarded as a three-dimensional Riemannian manifold and it is shown that the scalar curvature of a linear dynamical system $\text{d}x/\text{d}t=ax+by$, $\text{d}y/\text{d}t=cx+dy$ is non-positive. The manifold is scalar-flat iff $b=-c$ and $a=d=0$.