The rotation sets of most volume preserving homeomorphisms on \(\mathbb{T}^d\) are stable, convex and rational polyhedrons
From the summary: ``We consider volume preserving homeomorphisms of the torus \(\mathbb{T}^d\) \((d \geq 2)\) homotopic to the identity and prove that there exists a \(C^0\)-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.'' A very interesting aspect of this paper is that the authors overtake the homeo frame and they provide related results for continuous maps and general homeomorphisms homotopic to the identity.
scientific article; zbMATH DE number 7384523
scientific article