The asymptotic mean action and the asymptotic linking number for pseudo-rotations

2023/12/28 by Senior, David Bechara, Calvez, Patrice Le, Pirnapasov, Abror
#Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2312.17087

Abstract

We establish that the asymptotic mean action and the asymptotic linking number of irrational pseudo-rotations remain well-defined everywhere and constant for every C¹ irrational pseudo-rotation that behaves as a rotation on the boundary. As a consequence, we demonstrate that the isotopy of irrational pseudo-rotations with a positive rotation number is a right-handed isotopy in the sense of Ghys.

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