Rational Samuelson maps are univalent
type: Item
instance of: scholarly article
title: Rational Samuelson maps are univalent
zbMATH Open document ID: 0814.14049
DOI: 10.1016/0022-4049(94)90096-5
author: V. Pereyra
published in: Journal of Pure and Applied Algebra
publication date: 1994-04-04T00:00:00Z
review text: Let \(F = (f_ 1, \dots, f_ n) : \mathbb{R}^ n \to \mathbb{R}^ n\) be a differentiable map. \(F\) is called a Samuelson map iff all determinants \[ \mu_ r := \text{det}\left( {\partial f_ i \over \partial x_ j} \right)_{\begin{smallmatrix} 1 \leq i \leq r\\ 1 \leq j \leq r\end{smallmatrix}},\quad r = 1,\dots, n, \] are everywhere nonzero. The author proves the following theorem: Let \(F\) be a Samuelson \(C^ 1\)-map. If all functions \(f_ i\) have an algebraic graph then \(F\) is bijective. The author also deals with related questions, for instance the Jacobian conjecture. He gives many examples. Actually he proves stronger versions of the theorem.
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 13F50
Mathematics Subject Classification ID: 58C05
Mathematics Subject Classification ID: 58C25
zbMATH DE Number: 540915
zbMATH Keywords: Samuelson map
zbMATH Keywords: Jacobian conjecture
reviewed by: H.-J. Reiffen
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90096-5
OpenAlex ID: W2168255603
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description: scientific article; zbMATH DE number 540915