Effective algebraic geometry and normal forms of reversible mappings
type: Item
instance of: scholarly article
title: Effective algebraic geometry and normal forms of reversible mappings
zbMATH Open document ID: 1025.58018
published in: Revista Matemática Complutense
publication date: 2003-09-20T00:00:00Z
full work available at URL: https://eudml.org/doc/44427
review text: The authors consider a problem coming from the theory of discrete dynamical systems (iterations of diffeomorphisms in \({\mathbb R}^3\)). Namely, how to characterize the behaviour of the trajectories near the fixed points and the stability of this behaviour under perturbations. The authors use the computer in the context of reversible mappings. When such a mapping has some degree of degeneracy they apply Gröbner bases techniques and the theory of (formal) normal forms in the space of the coefficients of the jets of the mapping. They show that a language with typed objects like AXIOM is very convenient to solve such problems.
Mathematics Subject Classification ID: 58K50
Mathematics Subject Classification ID: 37C80
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 37C05
zbMATH DE Number: 1808648
zbMATH Keywords: Gröbner bases
zbMATH Keywords: (formal) normal forms
zbMATH Keywords: effective algebraic geometry
zbMATH Keywords: symbolic computation
zbMATH Keywords: reversible mappings
zbMATH Keywords: diffeomorphisms in \({\mathbb R}^3\)
author: Alain Jacquemard
author: Marco A. Teixeira
reviewed by: Vladimir P. Kostov
describes a project that uses: AXIOM
MaRDI profile type: Publication
DOI: 10.5209/REV_REMA.2002.V15.N1.16939
description: scientific article; zbMATH DE number 1808648