Hénon–Devaney like maps

Abstract:

We prove a general theorem characterizing the transitivity of homeomorphisms with singularities in the plane. We provide examples where this theorem applies including the classical Hénon–Devaney map (1981 Commun. Math. Phys. 80 465–476). We also prove some results about the plane homeomorphisms satisfying the hypothesis of our theorem namely the Hénon–Devaney like maps. Indeed, we show that the maximal invariant set of a Hénon–Devaney like map is topologically conjugated to a shift map. Furthermore, every Hénon–Devaney like map is fixed point free with dense periodic orbits. This generalizes some constructions by Devaney (1981 Commun. Math. Phys. 80 465–476) and Lenarduzzi (2015 Discrete Continuous Dyn. Syst. 35 1163–1177).

Año de publicación:

2021

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