Lyapunov exponents and the absolute continuity of intermediate foliations of special Anosov endomorphisms on T^d
DOI:
https://doi.org/10.12775/TMNA.2024.057Keywords
Anosov endomorphism, Lyapunov exponents, conjugacy, absolutely continuousAbstract
This work focuses on the study of Anosov endomorphisms of the torus $\mathbb{T}^d$ for $d \geq 3$. 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 $d \geq 3$, 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 \cite{Mic22measurable}.References
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Copyright (c) 2025 José Santana C. Costa, Fernando Micena
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