# Diffeomorphisms of Rn with oscillatory jacobians.

Waldyr M. Oliva; Nelson M. Kuhl; Luiz T. Magalhâes

Publicacions Matemàtiques (1993)

- Volume: 37, Issue: 2, page 255-269
- ISSN: 0214-1493

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topOliva, 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 -

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