The Hausdorff dimension of the Smale-Williams solenoid with different contraction coefficients

In this paper we prove that the Hausdorff dimension of the Smale-Williams solenoid $\overline {\Lambda }$ with different contraction coefficients $\lambda ,\mu$ is given by the formula $\dim _H(\overline {\Lambda } )=1+\frac {\log 2}{\log (1/\max (\lambda ,\mu ))}$. Further, for $\lambda ,\mu <\frac 18$ we prove that the Hausdorff dimension of each angular section is equal to $\frac {\log 2}{\log (1/\max (\lambda ,\mu ))}$.