We consider the rotation set ρ(Ф) for a lift Ф = (Фtt ∈ ℝ of a flow φ = (φtt: 핋2 → 핋2)t ∈ ℝ. Our main result is that ρ(Ф) consists of either a single point, a segment of a line through 0 with rational slope, or a line segment with irrational slope and one endpoint equal to 0. Any set of one of these types is the rotation set for some flow.
ASJC Scopus subject areas
- Applied Mathematics