S. Romaña

Affine Anosov Maps on $\mathbb{R}^n$: Classification, Index Spectrum, and Stability at Infinity

For $n\ge2$, we classify the affine diffeomorphisms $f_{A,v}(x)=Ax+v$ on $\mathbb R^n$ that admit a complete Riemannian metric with respect to which they are Anosov. Such a metric exists if and only if $A$ is hyperbolic or $f_{A,v}$ has no fixed point, equivalently $v\notin\operatorname{Im}(I-A)$. In the latter case, $...