A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• ISSN: 1815-0659
• Main Author: van der Kamp, Peter H.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211356
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves. Peter H. van der Kamp. SIGMA 17 (2021), 067, 14 pages

For cubic pencils, we define the notion of an involution curve. This is a curve that intersects each curve of the pencil in exactly one non-base point of the pencil. Involution curves can be used to construct integrable maps of the plane that leave invariant a cubic pencil.