Geodesic
On the Hyperbolicity of Toral Endomorphisms
Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 251-268.

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Nonsingular endomorphisms of the $m$-torus $\mathbb T^m$, $m\ge 2$, which are $C^1$ perturbations of linear hyperbolic endomorphisms are considered. Sufficient conditions for such maps to be hyperbolic (i.e., belong to the class of Anosov endomorphisms) are found.
Mots-clés : endomorphism, torus, Anosov endomorphism.
Keywords: hyperbolicity 
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A. Yu. Kolesov; N. Kh. Rozov; V. A. Sadovnichii. On the Hyperbolicity of Toral Endomorphisms. Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 251-268. http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a6/

[1] D. V. Anosov, “Geodezicheskie potoki na zamknutykh rimanovykh mnogoobraziyakh otritsatelnoi krivizny”, Tr. MIAN SSSR, 90, 1967, 3–210 | MR | Zbl

[2] F. Przytycki, “Anosov endomorphisms”, Studia Math., 58:3 (1976), 249–285 | DOI | MR | Zbl

[3] R. Mañé, C. Pugh, “Stability of endomorphisms”, Dynamical Systems – Warwick 1974, Lecture Notes in Math., 468, Springer, Berlin, 1975, 175–184 | DOI | MR

[4] K. Sakai, “Anosov maps on closed topological manifolds”, J. Math. Soc. Japan, 39:3 (1987), 505–519 | DOI | MR | Zbl

[5] A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “Ob odnom dostatochnom uslovii giperbolichnosti otobrazhenii tora”, Differents. uravneniya, 53:4 (2017), 465–486 | DOI | Zbl

[6] B. M. Levitan, Pochti-periodicheskie funktsii, GITTL, M., 1953 | MR | Zbl

[7] J. D. Farmer, E. Ott, J. A. Yorke, “The dimension of chaotic attractors”, Phys. D, 7:1-3 (1983), 153–180 | DOI | MR | Zbl

[8] M. Micena, A. Tahzibi, “On the unstable directions and Lyapunov exponents of Anosov endomorphisms”, Fund. Math., 235:1 (2016), 37–48 | MR | Zbl