On properties of the vertical rotation interval for twist mappings

Abstract

In this paper we consider twist mappings of the torus, T : T 2 → T 2 ,a nd their vertical rotation intervals ρV (T ) =( ρ − ,ρ + V ), which are closed intervals such that for any ω ∈) ρ − V ,ρ + V ( there exists a compact T -invariant set Qω with ρV (x) = ω for any x ∈ Qω, where ρV (x) is the vertical rotation number of x. In the case when ω is a rational number, Qω is a periodic orbit. Here we analyze how ρ − and ρ + behave as we perturb T and which dynamical properties for T can be obtained from their values.