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More integrable birational mappings
Physica A: Statistical Mechanics and its Applications, 1997We study birational mappings generated by matrix inversion and permutation of the entries of q × q matrices. For q = 3 we have performed a systematic examination of all the permutations of 3 × 3 matrices in order to find integrable mappings (of three different kinds) and finite order mappings.
N. Abarenkova +2 more
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Factorization properties of birational mappings
Physica A: Statistical Mechanics and its Applications, 1995Abstract We analyse birational mappings generated by transformations on q × q matrices which correspond respectively to two kinds of transformations: the matrix inversion and a permutation of the entries of the q × q matrix. Remarkable factorization properties emerge for quite general involutive permutations.
S Boukraa, J-M Maillard
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On cubic birational maps of $P^3_C$
Bulletin de la Société mathématique de France, 2016We study the birational maps of P 3 C. More precisely we describe the irreducible components of the set of birational maps of bidegree (3, 3) (resp. (3, 4), resp. (3, 5)).
Frédéric Han, Julie Déserti
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Some aspects of integrability of birational maps
2021In dieser Arbeit behandeln wir verschiedene Aspekte zur Integrabilität von birationalen Abbildungen, vorrangig im Kontext von Abbildungen, welche als Kahan-Diskretisierung von Systemen von quadratischen gewöhnlichen Differentialgleichungen gegeben sind.
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Nœther decomposition for birational maps
2013Let $ϕ$ be a birational map of the complex projective plane. We know that $ϕ$ can be written as a composition of automorphisms of $\mathbb{P}^2_\mathbb{C}$ and the standard quadratic birational map $σ$. This writing, that is non-unique, is minimal if the number $\mathfrak{n}(ϕ)$ of $σ$ is as small as possible. We prove that if $ϕ$ is of degree $d\geq 2$
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Birational maps and special Lagrangian fibrations
Proceedings of the Steklov Institute of Mathematics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Constructing quadratic birational maps via their complex rational representation
Computer Aided Geometric Design, 2021Xuhui Wang, Meng Wu, Qian Ni
exaly
On the Genus of Birational Maps Between Threefolds
2014In this note we present two equivalent definitions for the genus of a birational map \(\varphi: X --\rightarrow Y\) between smooth complex projective threefolds. The first one is the definition introduced by Frumkin [Mat. Sb. (N.S.) 90(132):196–213, 325, 1973], and the second one was recently suggested to me by S. Cantat.
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On the Construction of Elliptic Solutions of Integrable Birational Maps
Experimental Mathematics, 2017Matteo Petrera +2 more
exaly