Year: 2024
Type: article
Abstract: In this paper we introduce the concept of rotation cones, determined by rotation sets, and use these to describe the stability of rotation sets of incompressible and fixed-point free continuous flows on the torus $$\mathbb{T}^{d}$$ T d , d ⩾ 2. The previous concept is equivalent and extends the stability of rotation numbers (and rotation vectors) in the special case of fixed-point free continuous flows on $$\mathbb{T}^{2}$$ T 2 . We prove that incompressible Lipschitz vector fields with stable rotation sets have convex rotation cones with non-empty interior, and that all extremal edges are collinear with vectors in ℤ d . If, in addition, the rotation cones are proper, then these are polyhedral with finitely many edges. Finally we prove that the set of vector fields with stable rotation sets is C 0-open and dense among those having proper rotation cones.
Source: Israel Journal of Mathematics
Authors: Wescley Bonomo, Heides Lima, Paulo Varandas
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4403954770