The rotation sets of most volume preserving homeomorphisms on \(\mathbb{T}^d\) are stable, convex and rational polyhedrons
type: Item
instance of: scholarly article
title: The rotation sets of most volume preserving homeomorphisms on \(\mathbb{T}^d\) are stable, convex and rational polyhedrons
zbMATH Open document ID: 1482.37039
author: Wescley Bonomo
author: Heides Lima
author: Paulo Varandas
published in: Israel Journal of Mathematics
publication date: 2021-08-24T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 37E30
Mathematics Subject Classification ID: 37E45
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 37B65
Mathematics Subject Classification ID: 37B40
zbMATH DE Number: 7384523
zbMATH Keywords: volume-preserving homeomorphisms
zbMATH Keywords: torus
zbMATH Keywords: topological entropy
reviewed by: Juan L. G. Guirao
MaRDI profile type: Publication
full work available at URL: s11856-021-2148-7
OpenAlex ID: W3165391350
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DOI: 10.1007/S11856-021-2148-7
description: scientific article; zbMATH DE number 7384523