Finsler-Geometrical Approach to the Studying of Nonlinear Dynamical Systems

Abstract

A two dimensional Finsler space associated with the differential equation $y^{\prime \prime }=Y_3{y}^{\prime 3}+Y_2{y}^{\prime 2}+Y_1{y}^{\prime }+Y_0$ is characterized by a tensor equation and called the Douglas space. An application to the Lorenz nonlinear dynamical equation is discussed from the standpoint of Finsler geometry.

22 pages, Latex; Reports of Math. Phys.(1998)