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

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2021
• 1. Verfasser: van der Kamp, Peter H.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2021
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/211356
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.