We describe topological obstructions (involving periodic points, topological entropy and rotation sets) for a homeomorphism on a compact manifold to embed in a continuous flow. We prove that homeomorphisms in a $C^{0}$-open and dense set of homeomorphisms isotopic to the identity in compact manifolds of dimension at least two are not the time-1 map of a continuous flow. Such property is also true for volume-preserving homeomorphisms in compact manifolds of dimension at least five. In the case of conservative homeomorphisms of the torus $\mathbb {T}^{d} (d\ge 2)$ isotopic to identity, we describe necessary conditions for a homeomorphism to be flowable in terms of the rotation sets.

中文翻译：

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连续流产生很少的同胚

我们描述了用于嵌入连续流的紧凑流形上的同胚的拓扑障碍（涉及周期点、拓扑熵和旋转集）。我们证明了同胚$C^{0}$- 开放和稠密的同胚集同胚于至少维数为 2 的紧凑流形中的同一性不是连续流的时间 1 映射。这种性质也适用于维数至少为五的紧流形中的保体积同胚。在环面的保守同胚的情况下$\mathbb {T}^{d} (d\ge 2)$同位素到同一性，我们描述了同胚在旋转集方面可流动的必要条件。