Affine hyperbolic toral automorphisms (Q2631158)

Affine transformations of the torus with hyperbolic automorphism part are here shown to have dense periodic points and to be topologically transitive. Similar questions -- with more emphasis on the measurable properties like ergodicity and mixing -- were studied by \textit{F. J. Hahn} [Am. J. Math. 85, 428--446 (1964; Zbl 0161.34305)] and by \textit{H. Hoare} and \textit{W. Parry} [J. Lond. Math. Soc. 41, 88--96 (1966; Zbl 0136.11501); ibid. 41, 529--530 (1966; Zbl 0142.10303)].