We consider volume preserving homeomorphisms of the torus \({\mathbb{T}^d}\) (d ≥ 2) homotopic to the identity and prove that there exists a C⁰-open and dense subset of those homeomorphisms having stable rotation sets. Moreover, the rotation sets are polyhedrons with rational vertices and non-empty interior. Finally, we prove that the level sets in \({\mathbb{T}^d}\) formed by points that realize the extremal vectors carry zero topological entropy. We obtain related results for continuous maps and general homeomorphisms homotopic to the identity.

中文翻译：

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$$ {\ mathbb {T} ^ d} $$ T d上大多数体积保持同胚的旋转集是稳定的，凸的和有理的多面体

我们考虑圆环的体积保持同胚\（{\ mathbb【T} ^ d} \） （d ≥2）同伦到身份和证明了存在一个Ç ⁰具有稳定的旋转套那些同胚的-open和密集子集。而且，旋转集是具有有理顶点和非空内部的多面体。最后，我们证明了由实现极值向量的点组成的\（{\ mathbb {T} ^ d} \）中的能级集携带零拓扑熵。我们获得了有关连续图谱和与该身份同构的一般同胚的相关结果。