## Lyapunov exponent

if the Lyapunov exponent (L) = 0.9

and initial condition uncertainty = 0.1%

and we require that predictions of future behaviour in a system have errors less than or equal to 5%.

what is the time horizon (t) for making predictions?

I have been taught that t=(1/L)*ln(e/d(0)), where e=required accuracy of forecast, and d(0)=accuracy of initial measurement.

I'm assuming e=0.95, d(0)=0.99

Substituting what we have into the equation gives a negative value for t (t=-0.0559)

this seems wrong.

Am I using the formula correctly?

Any help would be appreciated!