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

Abstract

Let f f and g g be two Anosov diffeomorphisms on T 3 \mathbb {T}^3 with three-subbundles partially hyperbolic splittings where the weak stable subbundles are considered as center subbundles. Assume that f f is conjugate to g 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 [Discrete Contin. Dyn. Syst. 22 (2008), pp. 183–200]. Moreover, we get the same result for partially hyperbolic diffeomorphisms derived from Anosov on T 3 \mathbb {T}^3 .