Involutive birational transformations of arbitrary complexity in Euclidean spaces

Zdeněk Dušek; Oldřich Kowalski

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 1, page 111-117
  • ISSN: 0010-2628

Abstract

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A broad family of involutive birational transformations of an open dense subset of ℝ n onto itself is constructed explicitly. Examples with arbitrarily high complexity are presented. Construction of birational transformations such that φ k = Id for a fixed integer k > 2 is also presented.

How to cite

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Dušek, Zdeněk, and Kowalski, Oldřich. "Involutive birational transformations of arbitrary complexity in Euclidean spaces." Commentationes Mathematicae Universitatis Carolinae 54.1 (2013): 111-117. <http://eudml.org/doc/252538>.

@article{Dušek2013,
abstract = {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.},
author = {Dušek, Zdeněk, Kowalski, Oldřich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {rational mapping; birational transformation; involutive transformation; rational mapping; birational transformation; involutive transformation},
language = {eng},
number = {1},
pages = {111-117},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Involutive birational transformations of arbitrary complexity in Euclidean spaces},
url = {http://eudml.org/doc/252538},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Dušek, Zdeněk
AU - Kowalski, Oldřich
TI - Involutive birational transformations of arbitrary complexity in Euclidean spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 1
SP - 111
EP - 117
AB - 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.
LA - eng
KW - rational mapping; birational transformation; involutive transformation; rational mapping; birational transformation; involutive transformation
UR - http://eudml.org/doc/252538
ER -

References

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  1. Dolgachev I., Lectures on Cremona transformations, Ann Arbor-Rome, 2010/2011. 
  2. Dušek Z., Scalar invariants on special spaces of equiaffine connections, J. Lie Theory 20 (2010), 295–309. Zbl1206.53014MR2681371
  3. Dušek Z., Kowalski, O., Involutive automorphisms related with standard representations of SL ( 2 , ℝ ) , Bull. Belg. Math. Soc. Simon Stevin 19 (2012), 523–533. 
  4. Gómez A., Meiss J.D., 10.1088/0951-7715/17/3/012, Nonlinearity 17 (2004), 975–1000. Zbl1046.37024MR2057136DOI10.1088/0951-7715/17/3/012
  5. Hartshorne R., Algebraic Geometry, Graduate Texts in Mathematics, 52, Springer, New York-Heidelberg, 1977. Zbl0531.14001MR0463157
  6. Repnikov V.D., 10.1134/S0012266107100059, Differential Equations 43 (2007), no. 10, 1376–1381. Zbl1210.34014MR2397526DOI10.1134/S0012266107100059

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