| Title:
|
Involutive birational transformations of arbitrary complexity in Euclidean spaces (English) |
| Author:
|
Dušek, Zdeněk |
| Author:
|
Kowalski, Oldřich |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
111-117 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A broad family of involutive birational transformations of an open dense subset of $\mathbb R^n$ onto itself is constructed explicitly. Examples with arbitrarily high complexity are presented. Construction of birational transformations such that $\phi^k= \mathrm{Id}$ for a fixed integer $k>2$ is also presented. (English) |
| Keyword:
|
rational mapping |
| Keyword:
|
birational transformation |
| Keyword:
|
involutive transformation |
| MSC:
|
14E05 |
| idMR:
|
MR3038076 |
| . |
| Date available:
|
2013-02-21T14:09:43Z |
| Last updated:
|
2015-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143157 |
| . |
| Reference:
|
[1] Dolgachev I.: Lectures on Cremona transformations.Ann Arbor-Rome, 2010/2011. |
| Reference:
|
[2] Dušek Z.: Scalar invariants on special spaces of equiaffine connections.J. Lie Theory 20 (2010), 295–309. Zbl 1206.53014, MR 2681371 |
| Reference:
|
[3] Dušek Z., Kowalski, O.: Involutive automorphisms related with standard representations of ${\mathrm{SL}}(2,\mathbb R)$.Bull. Belg. Math. Soc. Simon Stevin 19 (2012), 523–533. |
| Reference:
|
[4] Gómez A., Meiss J.D.: Reversors and symmetries for polynomial automorphisms of the complex plane.Nonlinearity 17 (2004), 975–1000. Zbl 1046.37024, MR 2057136, 10.1088/0951-7715/17/3/012 |
| Reference:
|
[5] Hartshorne R.: Algebraic Geometry.Graduate Texts in Mathematics, 52, Springer, New York-Heidelberg, 1977. Zbl 0531.14001, MR 0463157 |
| Reference:
|
[6] Repnikov V.D.: On an involutive mapping of solutions of differential equations.Differential Equations 43 (2007), no. 10, 1376–1381. Zbl 1210.34014, MR 2397526, 10.1134/S0012266107100059 |
| . |
