A FINITE DIMENSIONAL PROOF OF A RESULT OF HUTCHINGS ABOUT IRRATIONAL PSEUDO-ROTATIONS

Patrice Le Calvez (1)

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

We prove that the Calabi invariant of a C 1 pseudo-rotation of the unit disk, that coincides with a rotation on the unit circle, is equal to its rotation number. This result has been shown some years ago by Michael Hutchings (under very slightly stronger hypothesis). While the original proof used Embedded Contact Homology techniques, the proof of this article uses generating functions and the dynamics of the induced gradient flow.

Mots clés: Irrational pseudo-rotation; Calabi invariant; generating function; rotation number; linking number MSC 2020: 37E30; 37E45; 37J11

Domaines: Systèmes dynamiques [math.DS]

Patrice Le Calvez. A FINITE DIMENSIONAL PROOF OF A RESULT OF HUTCHINGS ABOUT IRRATIONAL PSEUDO-ROTATIONS. 2022. ⟨hal-03853671⟩