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 Hnon–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 Hnon–Devaney like maps. Indeed, we show that the maximal invariant set of a Hnon–Devaney like map is topologically conjugated to a shift map. Furthermore, every Hnon–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).

我们证明了一个描述平面内奇点同胚的传递性的一般定理。我们提供了应用该定理的示例，包括经典的 Hnon-Devaney 映射 (1981 Commun. Math. Phys. 80 465–476)。我们还证明了满足我们定理假设的平面同胚的一些结果，即类 Hnon-Devaney映射。事实上，我们证明了 Hnon-Devaney 类映射的最大不变集在拓扑上与移位映射共轭。此外，每个类似 Hnon-Devaney 的地图都是固定点自由的，具有密集的周期轨道。这概括了 Devaney (1981 Commun. Math. Phys. 80 465–476) 和 Lenarduzzi (2015 Discrete Continuous Dyn. Syst. 35 ) 的一些构造 1163–1177）。