Wei, Kangning2022-02-102022-02-102022-02-051385-0172https://depositonce.tu-berlin.de/handle/11303/16341http://dx.doi.org/10.14279/depositonce-15116We constructed involutions for a Halphen pencil of index 2, and proved that the birational mapping corresponding to the autonomous reduction of the elliptic Painlevé equation for the same pencil can be obtained as the composition of two such involutions.en510 MathematikElliptic Painlevé equationhalphen pencildiscrete integrable systemManin involutionInvolutions of halphen pencils of index 2 and discrete integrable systemsArticle1572-9656