Abstract
We give an alternative proof of a theorem of Gambaudo and Ghys (Topology 36(6):1355–1379, 1997) and Fathi (Transformations et homéomorphismes préservant la mesure. Systèmes dynamiques minimaux. Thèse Orsay, 1980) on the interpretation of the Calabi homomorphism for the standard symplectic disc as an average rotation number. This proof uses only basic complex analysis.
Résumé
Nous donnons une preuve alternative d’un théorème de Gambaudo and Ghys (Topology 36(6):1355–1379, 1997) et Fathi (Transformations et homéomorphismes préservant la mesure. Systèmes dynamiques minimaux. Thèse Orsay, 1980) sur l’interpretation de l’homomorphisme de Calabi pour le disque symplectique standard comme un nombre de rotation moyen. Cette preuve utilise seulement l’analyse compléxe de base.
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References
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Acknowledgments
I thank Steven Lu for inviting me to give a talk on the CIRGET seminar in Montréal, that has lead me to revisit the theorem Gambaudo-Ghys and Fathi. I thank Albert Fathi for sending me his original proof of the theorem. I thank Boris Khesin for the Ref. [3].
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Shelukhin, E. “Enlacements asymptotiques” revisited. Ann. Math. Québec 39, 205–208 (2015). https://doi.org/10.1007/s40316-015-0035-5
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DOI: https://doi.org/10.1007/s40316-015-0035-5