A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves
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.
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211356 |
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| 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862603059557826560 |
|---|---|
| author | van der Kamp, Peter H. |
| author_facet | van der Kamp, Peter H. |
| citation_txt | 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 |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2026-03-14T03:21:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211356 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T03:21:08Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | van der Kamp, Peter H. 2025-12-30T15:54:58Z 2021 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 1815-0659 2020 Mathematics Subject Classification: 14E05; 14H70; 37J70; 37K60 arXiv:2009.09854 https://nasplib.isofts.kiev.ua/handle/123456789/211356 https://doi.org/10.3842/SIGMA.2021.067 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. The author is grateful for the useful and detailed comments made by the referees, in particular, for the further simplification of the map, and the comment about infinitely near base points. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves Article published earlier |
| spellingShingle | A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves van der Kamp, Peter H. |
| title | A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves |
| title_full | A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves |
| title_fullStr | A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves |
| title_full_unstemmed | A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves |
| title_short | A New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves |
| title_sort | new class of integrable maps of the plane: manin transformations with involution curves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211356 |
| work_keys_str_mv | AT vanderkamppeterh anewclassofintegrablemapsoftheplanemanintransformationswithinvolutioncurves AT vanderkamppeterh newclassofintegrablemapsoftheplanemanintransformationswithinvolutioncurves |