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June 2023
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5 Citations
Communications in Mathematical Physics
Let f be a non-invertible irreducible Anosov map on d-torus. We show that if the stable bundle of f is one-dimensional, then f has the integrable unstable bundle, if and only if, every periodic point of f admits the same Lyapunov exponent on the stable bundle as its linearization. For higher-dimensional stable bundle case, we get the same result on the assumption that f is a C1-perturbation of a linear Anosov map with real simple Lyapunov spectrum on the stable bundle. In both cases, this implies if f is topologically conjugate to its linearization, then the conjugacy is smooth on the stable bundle.