Enlacements asymptotiques revisit\'es

TL;DR

This paper provides a new proof, based on basic complex analysis, of a theorem relating the Calabi homomorphism to average rotation numbers in symplectic geometry.

Contribution

It offers an alternative, simpler proof of a known theorem, enhancing understanding of the Calabi homomorphism's interpretation.

Findings

New proof using basic complex analysis techniques

Clarifies the relationship between Calabi homomorphism and rotation numbers

Simplifies the original proof approach

Abstract

We give an alternative proof of a theorem of Gambaudo-Ghys and Fathi on the interpretation of the Calabi homomorphism for the standard symplectic disc as an average rotation number. This proof uses only basic complex analysis.