Rigidity of center Lyapunov exponents for Anosov diffeomorphisms on 3-torus

Daohua Yu, Ruihao Gu

Published 2022-10-23Version 1

Let f and g be two Anosov diffeomorphisms on T3 with three-subbundles partially hyperbolic splittings where the weak stable subbundles are considered as center subbundles. Assume that f is conjugate to g and the conjugacy preserves the strong stable foliation, then their center Lyapunov exponents of corresponding periodic points coincide. This is the converse of the main result of Gogolev and Guysinsky in [9]. Moreover, we get the same result for partially hyperbolic diffeomorphisms derived from Anosov on T3.