Robustly non-hyperbolic transitive endomorphisms on \(\mathbb{T}^{2}\) (Q2839315)

This paper deals with robustly non-hyperbolic transitive regular endomorphisms on \({\mathbb T}^2\). Let \(\mathrm{End}^*({\mathbb T}^2)\) be the set of regular endomorphisms on \({\mathbb T}^2\). Then the main theorem of the paper states: For any \(f\in \mathrm{End}^*({\mathbb T}^2)\), there exists \(g\in \mathrm{End}^*({\mathbb T}^2)\) such that \(g\) is homotopic to \(f\) and robustly non-hyperbolic transitive.NEWLINENEWLINEThree types of homotopy classes are distinguished. If contracting and expanding directions are involved, the authors trace the proof back to considerations in [\textit{N. Sumi}, Proc. Am. Math. Soc. 127, No. 3, 915--924 (1999; Zbl 0933.37012)]. The essential part of the proof is devoted the homotopy class containing non-hyperbolic linear endomorphisms. In this case, so-called blenders are used to construct corresponding robustly non-hyperbolic transitive endomorphisms. Finally expanding endomorphisms are considered.