Premium
Structural Stability of Constrained Polynomial Systems
Author(s) -
Llibre Jaume,
Sotomayor Jorge
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398004615
Subject(s) - mathematics , polynomial , ordinary differential equation , stability (learning theory) , differential (mechanical device) , differential equation , pure mathematics , mathematical analysis , computer science , engineering , machine learning , aerospace engineering
The structural stability of constrained polynomial differential systems of the form a ( x , y ) x ′+ b ( x , y ) y ′= f ( x , y ), c ( x , y ) x ′+ d ( x , y ) y ′= g ( x , y ), under small perturbations of the coefficients of the polynomial functions a , b , c , d , f and g is studied. These systems differ from ordinary differential equations at ‘impasse points’ defined by ad − bc =0. Extensions to this case of results for smooth constrained differential systems [ 7 ] and for ordinary polynomial differential systems [ 5 ] are achieved here. 1991 Mathematics Subject Classification 34C35, 34D30.