On roundness of rotation sets
Abstract
Abstract For a compact set L we define the roundness of L as the ratio between the area of L and the area of the smallest round disk containing L . Motivated by the question whether a round disk can be realized as the rotation set of a torus diffeomorphism, we study the roundness of rotation sets of a parametric family of torus diffeomorphisms F ρ , where the parameter ρ ranges over irrational numbers in ( 0 , 1 ) . With α m ρ := ⌈ m ρ ⌉ − m ρ for m ∈ N , each F ρ is a Kwapisz-like diffeomorphism with a 2-dimensional non-polygonal rotation set Λ ρ ′ = conv ( { ( ⌈ m ρ ⌉ − ⌈ m ′ ρ ⌉ m + m ′ + n + n ′ + 1 ,
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Analytic and geometric function theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- Physica Scripta
- Publisher
- IOP Publishing
- Volume
- 101
- Issue
- 27
- Pages
- 275209–275209
- Publication date
- 24 June 2026
- Language
- EN