• A FINITE DIMENSIONAL PROOF OF...

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

Title:
A FINITE DIMENSIONAL PROOF OF A RESULT OF HUTCHINGS ABOUT IRRATIONAL PSEUDO-ROTATIONS
Authors:
Le Calvez, Patrice
Contributors:
Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Publisher Information:
CCSD, 2022.
Publication Year:
2022
Collection:
collection:CNRS
collection:INSMI
collection:IMJ
collection:TDS-MACS
collection:SORBONNE-UNIVERSITE
collection:SORBONNE-UNIV
collection:SU-SCIENCES
collection:UNIV-PARIS
collection:UNIVERSITE-PARIS
collection:UP-SCIENCES
collection:SU-TI
collection:ALLIANCE-SU
collection:TEST3-HALCNRS
collection:SUPRA_MATHS_INFO
Subject Terms:
Irrational pseudo-rotation, Calabi invariant, generating function, rotation number, linking number MSC 2020: 37E30, 37E45, 37J11, [MATH.MATH-DS]Mathematics [math], Dynamical Systems [math.DS]
Original Identifier:
HAL: hal-03853671
Document Type:
Electronic Resource preprint<br />Preprints<br />Working Papers
Language:
English
Access URL:
https://hal.science/hal-03853671
https://hal.science/hal-03853671v1/document
https://hal.science/hal-03853671v1/file/Calabi4.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.hal.03853671v1
Database:
HAL

Further Information

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.