Rotation sets of toral flows

John Franks, Michal Misiurewicz

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)243-249
Number of pages7
JournalProceedings of the American Mathematical Society
Volume109
Issue number1
DOIs
StatePublished - May 1990

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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