SOLUTION

On a ${\bf w}(k\tau)=\lambda^k {\bf w}_0$ . Ainsi:

$\chi({\bf x}_0,{\bf w}_0)=\lim_{k\to +\infty}\frac{1}{k\tau}\ln (|\lambda_0|^k||{\bf w}_0||) =\lim_{k\to +\infty}\frac{k \ln |\lambda_0|}{k\tau} =\frac{\ln |\lambda_0|}{\tau}$ .