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We consider a dynamical system generated by a perturbation $A_\varepsilon$ ofan analytic Anosov diffeomorphism $A_0$ of $\mathbb{T}^d$. We show that, if$A_0$ admit a decomposition of $\mathrm T\mathbb T^d$ in $k$ invariantsubspaces, such a decomposition can be extended in an analytic way to$A_\varepsilon$. This implies that the Lyapunov exponents, if non degenerate,are analytic functions of the perturbation.

Analiticity of the Lyapunov exponent of perturbed toral automorphisms