TWIST MAPS OF THE ANNULUS: AN ABSTRACT POINT OF VIEW

Patrice Le Calvez (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We introduce the notion of abstract angle at a couple of points defined by two radial foliations of the closed annulus. We use this notion to give unified proofs of some classical results on area preserving positive twist maps of the annulus by using the Lifting Theorem and the Intermediate Value Theorem.

Mots clés: positive twist map; Birkhoff theory; region of instability; periodic orbit MSC 2020: 37E30; 37E40

Domaines: Systèmes dynamiques [math.DS]

Patrice Le Calvez. TWIST MAPS OF THE ANNULUS: AN ABSTRACT POINT OF VIEW. 2022. ⟨hal-03853661⟩