Dynamics of Local Groups of Conformal Mappings and Generic Properties of Differential Equations on~$\mathbb C^2$
Informatics and Automation, Nonlinear analytic differential equations, Tome 254 (2006), pp. 111-129
Voir la notice de l'article provenant de la source Math-Net.Ru
This paper is a survey of the present state of the problems related to the generic properties of foliations defined on $\mathbb C^2$ by algebraic differential equations. We prove that the properties of density, absolute rigidity, and existence of a countable set of complex limit cycles are inherent in all equations except possibly for the union of some real algebraic set and real analytic set of codimension at least two in the space of coefficients.
@article{TRSPY_2006_254_a3,
author = {A. A. Shcherbakov},
title = {Dynamics of {Local} {Groups} of {Conformal} {Mappings} and {Generic} {Properties} of {Differential} {Equations} on~$\mathbb C^2$},
journal = {Informatics and Automation},
pages = {111--129},
publisher = {mathdoc},
volume = {254},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a3/}
}
TY - JOUR AU - A. A. Shcherbakov TI - Dynamics of Local Groups of Conformal Mappings and Generic Properties of Differential Equations on~$\mathbb C^2$ JO - Informatics and Automation PY - 2006 SP - 111 EP - 129 VL - 254 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a3/ LA - ru ID - TRSPY_2006_254_a3 ER -
%0 Journal Article %A A. A. Shcherbakov %T Dynamics of Local Groups of Conformal Mappings and Generic Properties of Differential Equations on~$\mathbb C^2$ %J Informatics and Automation %D 2006 %P 111-129 %V 254 %I mathdoc %U http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a3/ %G ru %F TRSPY_2006_254_a3
A. A. Shcherbakov. Dynamics of Local Groups of Conformal Mappings and Generic Properties of Differential Equations on~$\mathbb C^2$. Informatics and Automation, Nonlinear analytic differential equations, Tome 254 (2006), pp. 111-129. http://geodesic.mathdoc.fr/item/TRSPY_2006_254_a3/