A note on the Jacobi stability of dynamical systems via Lagrange geometry and KCC theory

Abstract

If the matrix E is skew-symmetric it follows that the deviation tensor matrix P is also skew-symmetric because the Lagrangian d - torsion matrices are skew-symmetric (cf. above formulas). Consequently, the condition of odd dimensionality implies that the matrix P has its determinant equal to zero. In other words, the value  = 0 is an eigenvalue for the deviation tensor matrix P. It is obvious now that we obtain what we were looking for.