Lyapunov exponents and the absolute continuity of intermediate foliations of special Anosov endomorphisms on T^d - Costa, José Santana C.; Micena, Fernando (Topological Methods in Nonlinear Analysis, 2025)
This work focuses on the study of Anosov endomorphisms of the torus T^d for d ≥ 3. We aim to obtain metric and topological information about these endomorphisms by comparing their Lyapunov exponents with those of their linearizations. We provide a characterization of when the weak unstable foliation of a special Anosov endomorphism, which is close to a linear one, is absolutely continuous. Additionally, we demonstrate that in dimensions d ≥ 3, it is possible to find a smooth special Anosov endomorphism that is conservative but not Lipschitz-conjugate to its linearization. This contrasts with the smooth rigidity observed in dimension two, as described in Mic22measurable.