Title: On the Lipschitz equivalence of self-affine sets,
Abstract: Let $A$ be an expanding $d\times d$ matrix with integer entries and
${\mathcal D}\subset {\mathbb Z}^d$ be a finite digit set. Then the pair $(A,
{\mathcal D})$ defines a unique integral self-affine set $K=A^{-1}(K+{\mathcal
D})$. In this paper, by replacing the Euclidean norm with a pseudo-norm $w$ in
terms of $A$, we construct a hyperbolic graph on $(A, {\mathcal D})$ and show
that $K$ can be identified with the hyperbolic boundary. Moreover, if $(A,
{\mathcal D})$ safisfies the open set condition, we also prove that two totally
disconnected integral self-affine sets are Lipschitz equivalent if an only if
they have the same $w$-Hausdorff dimension, that is, their digit sets have
equal cardinality. We extends some well-known results in the self-similar sets
to the self-affine sets.