Abstract
AbstractWe 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.
Funder
DFG Collaborative Research Center
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Mathematical Physics
Reference9 articles.
1. Bayle, L., Beauville, A.: Birational involutions of $\mathbf{P}^2$. Asian J. Math. 4(1), 11–18 (2000). https://doi.org/10.4310/ajm.2000.v4.n1.a2
2. Carstea, A.S., Takenawa, T.: A classification of two-dimensional integrable mappings and rational elliptic surfaces. J. Phys. A (2012). https://doi.org/10.1088/1751-8113/45/15/155206
3. Hudson, H.P.: Cremona Transformations in Plane and Space. Cambridge University Press, Cambridge (1927)
4. Kajiwara, K., Masuda, T., Noumi, M., Ohta, Y., Yamada, Y.: Point configurations, Cremona transformations and the elliptic difference Painleve equation. Semin. Congr. 14, 169–198 (2006)
5. Kajiwara, K., Noumi, M., Yamada, Y.: Geometric aspects of Painlevé equations. J. Phys. A (2017). https://doi.org/10.1088/1751-8121/50/7/073001