Diffeomorphisms of Rn with oscillatory jacobians.

Oliva, Waldyr M., Kuhl, Nelson M., and Magalhâes, Luiz T.. "Diffeomorphisms of Rn with oscillatory jacobians.." Publicacions Matemàtiques 37.2 (1993): 255-269. <http://eudml.org/doc/41530>.

@article{Oliva1993,
abstract = {The paper presents, mainly, two results: a new proof of the spectral properties of oscillatory matrices and a transversality theorem for diffeomorphisms of Rn with oscillatory jacobian at every point and such that NM(f(x) - f(y)) ≤ NM(x - y) for all elements x,y ∈ Rn, where NM(x) - 1 denotes the maximum number of sign changes in the components zi of z ∈ Rn, where all zi are non zero and z varies in a small neighborhood of x. An application to a semiimplicit discretization of the scalar heat equation with Dirichlet boundary conditions is also made.},
author = {Oliva, Waldyr M., Kuhl, Nelson M., Magalhâes, Luiz T.},
journal = {Publicacions Matemàtiques},
keywords = {Difeomorfismos; Matriz jacobiana; Ecuación del calor; Problema de Dirichlet; oscillatory Jacobians; oscillatory matrix; transversality theorem; strictly totally positive matrix; spectral properties; diffeomorphisms},
language = {eng},
number = {2},
pages = {255-269},
title = {Diffeomorphisms of Rn with oscillatory jacobians.},
url = {http://eudml.org/doc/41530},
volume = {37},
year = {1993},
}

TY - JOUR
AU - Oliva, Waldyr M.
AU - Kuhl, Nelson M.
AU - Magalhâes, Luiz T.
TI - Diffeomorphisms of Rn with oscillatory jacobians.
JO - Publicacions Matemàtiques
PY - 1993
VL - 37
IS - 2
SP - 255
EP - 269
AB - The paper presents, mainly, two results: a new proof of the spectral properties of oscillatory matrices and a transversality theorem for diffeomorphisms of Rn with oscillatory jacobian at every point and such that NM(f(x) - f(y)) ≤ NM(x - y) for all elements x,y ∈ Rn, where NM(x) - 1 denotes the maximum number of sign changes in the components zi of z ∈ Rn, where all zi are non zero and z varies in a small neighborhood of x. An application to a semiimplicit discretization of the scalar heat equation with Dirichlet boundary conditions is also made.
LA - eng
KW - Difeomorfismos; Matriz jacobiana; Ecuación del calor; Problema de Dirichlet; oscillatory Jacobians; oscillatory matrix; transversality theorem; strictly totally positive matrix; spectral properties; diffeomorphisms
UR - http://eudml.org/doc/41530
ER -