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.
@article{urn:eudml:doc:41530,
title = {Diffeomorphisms of Rn with oscillatory jacobians.},
journal = {Publicacions Matem\`atiques},
volume = {37},
year = {1993},
pages = {255-269},
mrnumber = {MR1249230},
zbl = {0816.15021},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41530}
}
Oliva, Waldyr M.; Kuhl, Nelson M.; Magalhâes, Luiz T. Diffeomorphisms of Rn with oscillatory jacobians.. Publicacions Matemàtiques, Tome 37 (1993) pp. 255-269. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41530/