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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 067, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.067 (Mi sigma1749) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

Peter H. van der Kamp

Department of Mathematics and Statistics, La Trobe University, Victoria 3086, Australia
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DOI: https://doi.org/10.3842/SIGMA.2021.067
Abstract: For cubic pencils we define the notion of an involution curve. This is a curve which 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 which leave invariant a cubic pencil.
Keywords: integrable map of the plane, Manin transformation, Bertini involution, invariant, pencil of cubic curves.
Received: January 15, 2021; in final form July 2, 2021; Published online July 13, 2021
Bibliographic databases:
Document Type: Article
MSC: 14E05, 14H70, 37J70, 37K60
Language: English
Citation: Peter H. van der Kamp, “A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves”, SIGMA, 17 (2021), 067, 14 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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