Smoothness property for bifurcation diagrams.

Roussarie, Robert. "Smoothness property for bifurcation diagrams.." Publicacions Matemàtiques 41.1 (1997): 243-268. <http://eudml.org/doc/41294>.

@article{Roussarie1997,
abstract = {Strata of bifurcation sets related to the nature of the singular points or to connections between hyperbolic saddles in smooth families of planar vector fields, are smoothly equivalent to subanalytic sets. But it is no longer true when the bifurcation is related to transition near singular points, for instance for a line of double limit cycles in a generic 2-parameter family at its end point which is a codimension 2 saddle connection bifurcation point. This line has a flat contact with the line of saddle connections. It is possible to prove that the flatness is smooth and to compute its asymptotic properties.},
author = {Roussarie, Robert},
journal = {Publicacions Matemàtiques},
keywords = {Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Ciclos límite; Teoría de bifurcación; Puntos singulares; dynamical systems; two-dimensional autonomous ordinary differential equations; bifurcation},
language = {eng},
number = {1},
pages = {243-268},
title = {Smoothness property for bifurcation diagrams.},
url = {http://eudml.org/doc/41294},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Roussarie, Robert
TI - Smoothness property for bifurcation diagrams.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 1
SP - 243
EP - 268
AB - Strata of bifurcation sets related to the nature of the singular points or to connections between hyperbolic saddles in smooth families of planar vector fields, are smoothly equivalent to subanalytic sets. But it is no longer true when the bifurcation is related to transition near singular points, for instance for a line of double limit cycles in a generic 2-parameter family at its end point which is a codimension 2 saddle connection bifurcation point. This line has a flat contact with the line of saddle connections. It is possible to prove that the flatness is smooth and to compute its asymptotic properties.
LA - eng
KW - Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Ciclos límite; Teoría de bifurcación; Puntos singulares; dynamical systems; two-dimensional autonomous ordinary differential equations; bifurcation
UR - http://eudml.org/doc/41294
ER -