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In this paper, the general disagreement of the geometrical lyapunov exponentwith lyapunov exponent from tangent dynamics is addressed. It is shown in aquite general way that the vector field of geodesic spread $\xi^k_G$ is notequivalent to the tangent dynamics vector $\xi^k_T$ if the parameterization isnot affine and that results regarding dynamical stability obtained in thegeometrical framework can differ qualitatively from those in the tangentdynamics. It is also proved in a general way that in the case of Jacobi metric-frequently used non affine parameterization-, $\xi^k_G$ satisfies differentialequations which differ from the equations of the tangent dynamics in terms thatproduce parametric resonance, therefore, positive exponents for systems instable regimes.

General disagreement between the Geometrical Description of Dynamical  In-stability -using non affine parameterizations- and traditional Tangent  Dynamics