Structural stability of the inverse limit of endomorphisms (Q1683361)

The paper proves that every endomorphism that satisfies Smale's Axiom A and the Strong Transversality condition is \(C^1\)-inverse limit structurally stable. This fact, along with previous works [\textit{N. Aoki} et al., Fundam. Math. 169, No. 1, 1--49 (2001; Zbl 1031.37021); \textit{P. Berger} and \textit{A. Rovella}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 3, 463--475 (2013; Zbl 1373.37096)], proves that \(C^1\)-inverse limit stable covering maps of manifolds are exactly the \(C^1\)-covering maps which satisfy Axiom A and the Strong Transversality Condition. The result is applied to the study of unfolding of some homoclinic tangencies.