arXiv subjects
Publications and source records attributed to Vítor Araújo.
For any dimension $d\geq 3$ we construct $C^{1}$-open subsets of the space of $C^{3}$ vector fields such that the flow associated to each vector field is Axiom A and exhibits a non-trivial attractor which mixes exponentially with respect to the unique SRB measure.
It is proved that an endomorphism $φ$ of a hyperbolic group $G$ satisfies a Hölder condition with respect to a visual metric if and only if $φ$ is virtually injective and $Gφ$ is a quasiconvex subgroup of $G$. If $G$ is virtually free or torsion-free co-hopfian, then $φ$ is uniformly continuous if and only if it it satisfies a Hölder condition if and only if it is virtually injective. Lipschitz conditions are discussed for free group automorphisms.
Four geometric conditions on a geodesic metric space, which are stronger variants of classical conditions characterizing hyperbolicity, are proved to be equivalent. In the particular case of the Cayley graph of a finitely generated group, it is shown that they characterize virtually free groups.