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In our paper (V. I. Arnold and Ya. G. Sinai, “On small perturbations of automorphisms of the torus”), published in *DAN*, vol. 144, no. 4, 1962, the smoothness of the curves considered in Theorem 1 is insufficient for applying Theorem 2 in the proof of Theorem 3. Theorem 3 itself, however, is valid, as follows from D. V. Anosov’s work “Roughness of geodesic flows on compact manifolds of negative curvature” (*DAN*, vol. 145, no. 4, 1962).
V. Arnold
Submitted 1963-01-01 | RussiaRxiv: ru-196301.67283 | Translated from Russian

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In our paper (V. I. Arnold and Ya. G. Sinai, “On small perturbations of automorphisms of the torus”), published in DAN, vol. 144, no. 4, 1962, the smoothness of the curves considered in Theorem 1 is insufficient for applying Theorem 2 in the proof of Theorem 3. Theorem 3 itself, however, is valid, as follows from D. V. Anosov’s work “Roughness of geodesic flows on compact manifolds of negative curvature” (DAN, vol. 145, no. 4, 1962).

V. Arnold
Ya. Sinai

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[v1] 1963-01-01

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In our paper (V. I. Arnold and Ya. G. Sinai, “On small perturbations of automorphisms of the torus”), published in *DAN*, vol. 144, no. 4, 1962, the smoothness of the curves considered in Theorem 1 is insufficient for applying Theorem 2 in the proof of Theorem 3. Theorem 3 itself, however, is valid, as follows from D. V. Anosov’s work “Roughness of geodesic flows on compact manifolds of negative curvature” (*DAN*, vol. 145, no. 4, 1962).